Nothing scared the British and Americans more than the prospect of the Soviets making a separate peace. To prevent it, Lend Lease would have been stepped up and action taken on the continent (perhaps in the Balkans or southern France or even in Norway--to cut off crucial Swedish supplies to Germany--but perhaps also on the Atlantic coast of France
The Allies finished off the Axis in North Africa before Kursk and landed in Sicily around the same time. IIRC Lend Lease had already been stepped up when removal of Germans from the Caucasus area enabled the allies to send more supplies via the Persian gulf. I think the Allies were doing all they could pretty much as fast as they could but Stalin still wasn't satisfied until D-Day.
Dieppe btw showed it was unwise to land in France without lengthy, careful preparations.
to draw enough Germany troops west and/or south to give the Soviets breathing room (meaning, no attack on Moscow). And the bombing campaign against Germany and the Rumanian oil fields would be stepped up, regardless of the cost, to keep the Germans from exerting effective air power on the Eastern front. So Kursk would end up not as a pyrrhic victory but rather as a tour de force that goes nowhere. And Stalin would get what he wanted: Western allies with more boots on the ground earlier than 1944 and more equipment for his own armies. I think how the Allies react to the hypothesized Manstein victory would make a fascinating scenario.
I dunnoo.... had the Germans won at Kursk with minimal/acceptable losses, the Soviets would probably have become demoralized or gotten ideas. Stalin might've reasoned that if he made a separate peace, the Germans and western allies would beat themselves up for a year or two so a rebuilt Soviet army could then recapture remaining occupied territories with ease and even sweep into eastern Europe.