Could they, how would they have handled their pilots, flying the same number of missions as their Luftwaffe counterparts?
They wouldn't, purely because the Western Allies had the necessary resources that they didn't need to do it and it was a very silly way to run an airforce.
The only way it would be historically feasible - forget necessary for a second - would have been if they'd drastically cut back on pilot training schools and thus didn't have the required number of trained pilots coming through to replace those leaving at the end of their tours.
Otherwise, if Allied fighter pilots had hung around like Luftwaffe pilots, you'd see some racking up bigger scores (but never on the scale of the Luftwaffe, purely because there weren't the scoring opportunities), others ending up as KIA/WIA/MIA/PoW and others being invalided out with PSTD. Their chance of survivability was probably pretty high, particularly from the beginning of 1943 onwards, purely because of the size of the Allied airforces.
Bomber pilots would be faced with a much less enviable prognosis. Flak remained just as deadly throughout the war in daylight, and it was much more a matter of inevitability that you were going to get hit eventually. Night bombing was almost as costly in terms of loss rate (sometimes better, sometimes worse), so again it becomes a matter of "when, not if" when pilots are forced to fly until they can't fly any more.
The main issue I can see is morale. I get the feeling that in the RAF the euphamism "Lack of Moral Fibre" covering psychological prblems, morale issues and outright cowardice would have become much more prevalent. The USAAF took a more scientific approach to the issue, as was their want on a lot of things related to pilots and piloting, but I cant see their pilots escaping the 'fly until you die situation' much less unscathed than RAF ones.