Certainly yes. The Soviets could of course themselves produce radios, cables, radars and high octane fuel but would have to divert significant production capacity from military hardware like tanks, guns and planes. I think especially the high octane fuel is critical. It is not that easÿ to produce but without it your planes have a huge handicap.
http://www.oilru.com/or/47/1006/
The link above has some interesting figures (and also get the number of German Divisions wrong - misprint?) but I think it point to the critical value of High Octane fuel in LL deliveries - especially in the first critical years of the war. That could very well be decisive - not necessarily in like the SU being annihilated, but I'm not sure the Soviet leadership could have taken that many more defeats, or absence of victories, without asking for a separate peace.
They could make up
some of the difference, but not even most of it. They have a limited surviving industrial capacity and in the case of high octane fuel a limited pre-war production capacity. So unless the US ships them the machinery to expand production capacity, they can only really make a fraction of what they got via LL and in terms of fuel without the US grade avgas or other high octane fuels the Soviets can't use American or British vehicles, whether AFVs, trucks, or aircraft. The Germans found that Soviet fuel wouldn't even work in their vehicles in 1941 because it was so low grade, so required additives to get it to work. They will have a major handicap through the rest of the war as a result. Again I'm talking about OTL after the invasion ravaged Soviet production abilities; had they preserved their pre-war industry they should have been able to meet most of their needs.
How would the Soviet fare against Nazi if LL to them excluded the things that I mention in the thread title? I don't really believe that the lack of LL supply of these equipment would make them lose the war (unlike food or railroad equipment), but would this significant slow down Soviet victory?
Its not necessarily fatal, but it does preclude major advantages of LL in the later stages of the war. As I said above losing certain fuel grades would make the use of US LL vehicles impossible. So I'm assuming you mean just Avgas, not all improved fuel grades? Or that they send additives so that Soviet fuels work in US vehicles minus aircraft? You kinda have to include high performance fuels in LL if you want finished weapon systems like vital AFVs and aircraft (from the US and UK) to work, while some sort of LL additives would be necessary to make Soviet fuel work in trucks. So you'd have to exclude a huge, vital part of LL to remove all those transport and weapon systems are a result of lack of fuel. So you might want to walk that part of OP back.
That said the lack of communications gear with hurt a LOT. Especially for Deep Operations, because Soviet comm equipment was not that great and relied on LL supplied subcomponents that they couldn't make for themselves after the Germans overran so much of their pre-war industry (not that Soviet grade subcomponents were particularly great, so the US/UK parts actually stepped up Soviet quality equipment). Electronics was the one area even the pre-war USSR was lagging in badly. They were behind even the French and Japanese in radar as of 1941, had nowhere near enough radios in 1941 for even their standing army (let alone regular equipment), and the quality of the radios was below European standards. That was a serious problem that continued to the end of the Cold War in the USSR; they were good at many things including heavy industry but their electronics industry and developments were really lagging compared to the other major powers. They could reverse engineer captured Allied (they literally stole a British radar on a merchant ship in Murmansk and disassembled it before returning it) and German radar and electronics and produced their own improved models (with LL help in terms of sourcing components), so the issue is not that they couldn't figure things out, just that they weren't advanced enough in domestic developments and never really caught up in the Cold War for a variety of reasons.
So losing the numbers and quality of LL communications equipment will not be made up even by diverting increase raw materials and manpower to the electronics industry, especially as it was maimed by Barbarossa. So like in 1941-42 when say tank units only had a battalion commander with a radio that problem would continue on throughout the war without LL comm equipment. Which means a ton more losses, highly vulnerable units if anything happened to the commander's comm equipment, a major inability to exploit deeply breakthroughs because of lack of ability to communicate success, developments, receive orders, coordinate, or even request air support. Landlines were fine for static/retreating situations, but mobile offensives need radios. You can strip them from all foot infantry units to concentrate them in mobile ones, but penetrations will have to be more shallow due to limit numbers of radios or ability to rapidly extend land lines without US copper wire, which means a more limited advance, higher losses, and for the foot infantry much higher losses due to lack of communication and reversion to WW1 techniques to say communicate with artillery (flares and runners).
Not having radar isn't really that important TBH given the nature of the Eastern Front, so I won't comment there it just make certain things somewhat more vulnerable, but given that the US and UK drew off most German aircraft by 1943 anyway and what the Germans left behind in the East generally didn't stray into range of Soviet radar IOTL by 1944 it won't really be that significant of an impact. The Luftwaffe was dying in the West anyway and what was left in the East was an annoyance, not a major threat by 1943 to the Soviets.
Lack of radio will hurt a lot though, perhaps more than anything. CiC was vital to success in the offensive and a if not the major reason Germany did so much better than her opponents in 1939-42. Being able to coordinate because of the advantage of greater communications equipment is enormous. The US demonstrated that from 1943-45 with even platoon leaders having 'walkie-talkies' and ability to send artillery fire and air strike requests, plus stay in contact with command. You can have firepower dominance over your foe, but if you don't have the ability to coordinate it's use you can't really take advantage of it. It was part of the reason Soviet artillery under performed relative to German artillery throughout WW2 (the other was lack of highly trained artillerists and some equipment to improve speed of response), as they were just not flexible like the Wallies in their ability to use it. The mastered their pre-planned methods and maximized their advantages while minimizing their disadvantages, but the ability to respond to non-preplanned fire missions was very slow. Without radios they will be even more limited.