Hmm....
This could be part of Hitler's attempts to "woo" the UK. He'd already let on as to how Germany had no actual desire to the fight the British, they just wanted justice against the French and a free hand on the Continent. The UK could have its Empire with no need for any quarrel between the British and German peoples. This all being just as devout and truthful a promise from Adolf as any of his others...
Without the Blitz there'd be less ire from the average Briton aimed toward Germany. This, much like there was less ire from the average German directed at the English until the RAF began burning down Germany's cities. The support for the Nazi Party actually increased after that as a feeling of national unity due to a common threat took hold in Germany. The same thing had happened in England due to the Blitz. No Blitz and there'd be less of that national unity in the UK and more of an attitude of "it's not our fight and the Germans aren't really our enemy" would be more prevalent.
With some adroit propaganda on the Nazi's part they could parlay this into making it very difficult for Churchill to increase the war's scope against Germany. This, especially in support of Communist Russia. The Nazis did, in OTL, try and portray their war against the Soviets as being some sort of a "valiant struggle of Western values and freedoms against the evil Bolshevik hordes!" That message fell rather flat as Britons looked out at their charred cities from the latest round of Luftwaffe bombings.
Thus Germany might find itself with all those "extra" pilots, aircraft, and fuel facing a Soviet Union that is even more isolated than in OTL as Churchill might not be able to justify supporting the USSR in the face of a more "peaceful" Nazi Germany. The threat of Germany's unleashing its "mighty Luftwaffe" against the UK could be quite the lever to that end.
Yes, there would be less escalation of bombing as the Germans have better bases and more planes and the British who aren't being bombed would fear retaliation.
I suspect additional German/Italian air power and attention in the med would in general cancel out additional British forces that could be placed there. But the British would win victories, certainly Italian East Africa would fall, keeping British public support up in the war for a while anyway. There probably isn't much incentive if not under any threat to make peace, and its not been long enough for apathy to set in, so I doubt if any peace movement breaks out.
I suspect the additional German aircraft means Leningrad would fall in 1941 and perhaps Sevastopol as it would be easy to supply the extra aircraft in those areas. It would also allow additional aircraft in the October 41 on time frame around Moscow as attrition and withdraws to the Mediterranean shrunk the German aircraft pool more than supply constraints. This likely means the Soviet counterattack is lessened as the Soviet have to commit more reserves early to defense and the Germans are able to put up more air power in the winter (and maybe Lend Lease is delayed a month or two if the British as you suggest adopt a more wait and see attitude torward the Soviets). I suspect once the Soviets stop the Germans in December, (and the USA is in) the British will be all in as in OTL.
But the Germans are in better shape in 1942 on the eastern front, probably leading to a stalemate grinder from November 1942 until September 43, vs an epic Stalingrad like fail, but by then Italy's withdrawal means the force ratios are well in the Soviets favor by then.