nope - no piston engine fighter can outrun the me262 in the air (starting and landing take beside - but for this you do not need such hyper plane)
sure could the allies discover the whole concept at their own - but also could the green aliens from mars be allied with the nazis or hitler, deciding he need the bomb let some supergermans produce em in a few weeks... it is possible only if you go asb. So sorry, no.
IN this plot the allies suffer badly cause they do not develop (like they did historically) the right technology... like the germans missed the radar train or the nuclear weapon train...
to change this is asb. Like "japan beat USA in pacific war" - possible? yes, but not in a realistic scenario...
Greetings
Discovering swept wings isn't something just the Germans can do. It would've been discovered with or without the help of Germans. If we had to discover it by looking at German planes, we could(The Soviets got many technologies from looking at our planes, trust me, and we did the same. The F-15 probably benefited from data about the MiG-25 obtained when a soviet pilot defected in a Mig-25. Notice the intake similarity? The Soviets used that intake style first. Copying is VERY important in R&D.). And a select few PRODUCTION P-80As were flying in '45, while we were still at war with Germany. P-80A was made by Americans. The F-86 was where German scientists really helped us alot.
And you don't have to be faster to win in the air. It comes down to many other factors, mainly skill. You're thinking 100-200 MPH is going to make the german fighters invincible. Far from it. Speed isn't everything. For example, in Vietnam, US supersonic fighters were many times downed by subsonic Mig-17s, which were considered more obsolete compared to supersonic fighters with missiles(Except the F-105, on bombing missions they basically only had the gun for defense) and reliable engines than the P-51 was compared to the Me-262. I believe Skyraiders and
AH-1s managed to down Mig-17s or Mig-21s occasionally with unguided rockets or their gun.
Also, as CalBear said, swarm tactics. Brutally effective.