Unquestionably. But - a large part of the Panzertruppen were committed to the defense of the West before the invasion. So it does not seem likely that all of those 2,200 AFVs would have been in the east, or been sent east, even if the US/UK held back from OVERLORD. Assume that something really bizarre happens in May 1944, and the US/UK cancel OVERLORD. The Germans won't know, unless the decision is publicly announced, and so there will be no effect on at least the first half of BAGRATION. All reserves and reinforcements that went west will go east, of course.
Eventually, some forces will be transferred from west to east. The actual catastrophe in the east will loom much bigger when there is no fighting in the west. But how many and when is debatable: the threat in the west will remain. Probably the Germans will strip the western defenses down to the infantry in the static coastal divisions, which will be allowed to "run down".
The western divisions will get no replacements at all, and even units that are static, and not engaged at all, lose a trickle of men: accidents, illness, desertion, transfers, discharges. Maybe 2-3% a month, which over six months starts to add up.
Right, but I thought I made clear that using the entire strength in the East probably wouldn't happen (though IIRC the window to invade was closing so if not by June 6th or so then it was impossible until July, which gives the chance to use the OKW strategic reserve in the East). That leaves the strategic reserve for use in the East if the Wallies are in the war, potentially more if for some reason say the US wasn't involved, that there is no invasion in the West. By late June the strategic reserve would have to be used in the east, which means at least half of it, 3 Panzer divisions, most prepared to go.
Actually looking back at the history, 9th and 10th SS divisions were already in the East and IOTL on June 12th sent to Normandy from Ukraine to help counter the invasion. So they would stay put and get transferred to Belarus instead without Normandy. That's 2 divisions right there, but both were worn from fighting in Spring. They probably get sent with 5th Panzer then. 1st SS division was probably the easiest of the Western divisions in OKW reserve, which means it gets sent East first at the same time as the shift to defend Minsk happens. IOTL IIRC 5th and 12th Panzer divisions were sent, while ITTL 9th and 10th SS Panzer divisions could/would also be sent, with the 1st SS Panzer Corps (1st SS, 12th SS, 17th SS, and Panzer Lehr, the Western Front's strategic reserve) potentially being sent en masse or broken up and partially sent.
In terms of the invasion the Germans thought that the weather was going to be too bad for the rest of the month for an invasion to be possible, which is why Rommel was away on leave when the invasion happened IOTL:
https://en.wikipedia.org/wiki/Erwin_Rommel#Atlantic_Wall_1944
The 5 June storm in the channel seemed to make a landing very unlikely, and a number of the senior officers were away from their units for training exercises and various other efforts. On 4 June the chief meteorologist of the 3 Air Fleet reported that weather in the channel was so poor there could be no landing attempted for two weeks. On 5 June Rommel left France and on 6 June he was at home celebrating his wife's birthday.
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With things getting bad for AG-Center I could easily see Hitler taking that information and at least sending the most ready divisions East even with already dispatching the II SS Panzer Corps (9th and 10th SS) ITTL. So I could see Panzer Lehr going at a minimum to reinforce II SS Panzer Corps and perhaps then 1st SS, leaving half of the 1st SS Panzer Corps as a strategic reserve just in case. That still leaves the West with a lot of defensive strength in terms of armor if needed, but I could also see Hitler getting desperate and continually stripping out the west to shore up the east.
So would you say it is fair that without Normandy happening, let's say things are delayed two months due to a storm smashing up landing craft and damaging the Mulberry harbors, and Hitler feels that the immediate situation demands it and the weather situation being what it is, so in addition to sending the historical reinforcements also dispatches I SS Panzer Corps from France (4 Panzer Divisions) and II SS Panzer Corps (2 division) from Ukraine? 6 divisions would be necessary to save what's left of AG-Center, but that leaves several Panzer divisions with the West, just depriving them of the 4 in strategic reserve that were there, plus the 2 that were brought in from the East after the Wallies landed.
Edit:
I'm figuring that the first wave of support arrives as per OTL, but due to reinforcements 5th and 12th Panzer are used together to defend against 5th Guards Tank Army, while the II SS Panzer Corps (9th and 10th SS) are used south of Minsk to hold the line (or vice versa) and relieve the 383rd infantry division at Bobruisk and check the Soviet 65th army, et al, coming up from that direction (there were additional German units in the area at the time to help too). They may be shifted before June 26th too, the date 5th Panzer was transferred (arriving on the 27th), to support AG-Center.
https://upload.wikimedia.org/wikipe...gration_minsk_pocket_1944_june_29-july_03.png
5th and 12th Panzer divisions would then fight together at Borrisov, where, if they could hold the line, would prevent what remained of 4th Army in the center from collapsing when it's flanks were pushed in IOTL. That should buy time for the I SS Panzer Corps to show up with some air support and derail the Bagration plan to encircle AG-Center entirely, though they will certainly smash it up pretty badly. Then the two SS Panzer Corps are stuck in the East and will not be available for the West if/when the Wallies move (if they do ITTL).