If Italy stays neutral that could benefit Germany. If there’s no major fighting in Africa due to Germany not having much of a feasibly way to get there as Italy would be cut off. Plus IIRC Germany didn’t want to focus on Africa but rather Russia and was dragged in by Italy.
Without a war in Africa and Italy more troops and Erwin Rommel gets sent to Russia. I’m not an expert on military history so I don’t know how the war would go in Russia but it could with Rommel and more men and equipment go much better for Germany. If they could take Moscow that would be a major blow to the Soviet’s as the cultural hub was taken along with it being an industrial hub, crippling morale and weakening the industrial capabilities of the Soviets.
Germanies' overall big problem in Barbarossa is not a lack of men/tanks. They start of with numerical superiority, and once they lose it which they do pretty quick they're losing it by far more than what Afrika corp can supply. (as pointed out the DAK doesn't get above
approx. 10 German divs even later, so compared to Barbarossa's opening 160+ divs they're not adding much.
Germany has two big problems in Barbarossa one with a flawed goal based on a flawed understanding of the situation, and the second with operational issues if the plan doesn't go exactly as planned in the time frame that's planned. (and so the former impacts on the latter) neither is improved by a few more Divs.
the issue with the extra forces of Rommel and the Afrika Corp allows Germany to take Moscow idea is:
1).Moscow was never a primary goal of the plan, it at times was moved up the priority list as the actual goal (destroy the red army) looked less and less achievable as time went on but Moscow as possible primary stepping stone to victory went by the wayside fairly early on in planning (even if some figures had been more pro the idea and had kept it mind). Ultimately the German attitude towards Moscow was "we should already have won by the time we're taking Moscow", not "taking Moscow is how we win". So no one in German high command is going to take those extra divs in May41 and decide with these extra forces we can now take Moscow.
2). You'd still have to get those* extra forces to Moscow and in a condition to take it. two big problems with this firstly the logistical and terrain issues that are still there (in fact made worse by feeding another 10 divs into it). But also the forward panzer divs which were always the minority of the total German forces had instead of successfully avoiding head on fights in a short fast campaign (as per Blitzkrieg) had to fairly often fight through Soviet lines and had been doing so for months. Now they had done so and won those engagements, but after a few months of near constant fighting and losses they were seriously depleted.
Frankly the Afrika corp risk just being more tanks and troops stuck in the mud and waiting for fuel and counting their casualties, while writing home about how the red army should have run out of troops a month ago so where the fuck are all these Russians coming from and why are they still fighting.
*it doesn't have to be precisely those Divs under Rommel doing it, but the general point is that bit extra at the start allows it to happen.