While the USA might, in this scenario, be responsible for the garrisoning of Iceland, and possibly respond to Portuguese "requests" for troops for the Azores, a USA that does not get in to the war in Europe absent PH etc is not going to send large numbers of troops to garrison Iraq or Egypt, or anywhere else. To the extent the US presence in this scenario is going to be increased it would be to increase the troops in the PI and other Pacific islands, as was underway OTL, the Canal Zone, and perhaps a few other spots OF TERRITORY BELONGING TO THE USA!
You are aware, of course, that Iceland was not a US possession, a US mandate, or in the Pacific, and that the occupation of it with US troops began while the USA were neutral.
Absent the USA being in the war sending tens of thousands of troops as well as air support to far away places where they are likely to be attacked is simply not politically possible.
You are aware, of course, that in 1941, before December, US armed forces were regularly sent to places where they were very likely to be attacked. That actually did happen in September and October 1941, and in October there were some 100 KIAs, with the USA still neutral.
Protecting US possessions, yes, protecting the colonial possessions of the UK and France - no way. On top of the political reality, this would mean expanding the draft and service limits (only done by one vote OTL) in a peacetime environment as well as equipping and supplying these troops. Of course, there is the thorny issue about who controls these troops now stationed on UK/French territory.
That, of course, depends on how one reads the intention of the Administration at the time. The deployment of US Navy assets to combat zones where they were indeed attacked, the occupation of Iceland, the very novel concept of the "neutrality patrols", the violation of the duties of a neutral, and other similar signs seem to point out the rather evident fact that the US government
wanted war. If for some reason Roosevelt cannot get that, then he might well go to some unprecedented "short of war" measures. If you described Lend-Lease as per OTL to an OTL US senator in say 1936, I'd bet he'd say "no way this is going to happen".
While no active Pacific War means assets used OTL don't need to be sent there, the Japanese are still a threat so you can't simply leave the area with a few rowboats and unarmed bobbies to represent Imperial interests. Yes, you'll certainly get more ANZAC forces in Europe and keep more UK forces there than OTL with no war in the Pacific. Still a major manpower deficit once you start talking about invading Sicily/Corsica/Sardinia, let alone the Italian mainland or France and likewise all the USAAF contributions from late 1942 onwards.
The US contribution to Operation Husky was roughly equivalent to the British troops deployed in Malaya and Singapore (and nearly entirely lost to the Japanese), even though qualitatively it was better. The manpower deficit will possibly be felt once one considers Avalanche and Overlord, yes. But then again, as mentioned, in this ATL you will also have lots of Soviet divisions moving from Vladivostok to Kursk. Nobody says the Western and Eastern Allies have to meet along the same OTL line.
As to the air war, dont' forget that there is no Battle of the Atlantic. Coastal Command will really be the poor relations here.
I very much doubt the UK will be able to make up the numbers (even just for infantry) by "importing" troops from India. However negative Gandhi and the INC and others were about Indian troops fighting, even against the Japanese on their door step, imagine the agitation if Indian troops are sent in truly massive numbers (compared to OTL) to Europe to die not even to protect India but for "British Imperialism".
Indian politicians will be unhappy. And...? Also let's not forget that the Indian Army was the largest
volunteer force in the war. I think between 2.5 and 3 million men. And nobody "sent" anybody nowhere against their will.
Yes, the LL work boosted US employment and was a plus for the economy. However SOMEBODY had to pay for all this industrial activity, and it wasn't the British, French, or Russians. Essentially every bit of LL production was paid for by the US government, subsidized by the US population through taxes, bond drives, and inflation. Since the USA was in the war, and giving allies LL materials from SPAM to aircraft meant that the toll among US forces was decreased, these sacrifices on the part of the US population were pretty universally accepted. With no USA in the war, selling these sorts of sacrifices...
We must have a different idea of sacrifices. As of now, I own some state securities, and they pay me interests. I don't see that as a sacrifice but as an investment for the future that will be good for my pockets. Certainly, it's state deficit; the state is borrowing from me. It's a policy that was not unknown in the USA in the 1930s. I'm also paying lots of taxes, of course.