No. The Gloster Meteor first flew in '43, and for the entirety of the war the RAF had one operational squadron of them, which stayed over the Isles for fear of the Germans shooting one down and capturing the wreckage.
No, it was because he thought a faster flying bomber could penetrate air defenses and GTFO better than existing ones. He wasn't wrong on that idea, but the Schwalbe wasn't the right airframe for that job. However, the Germans were also working on other jet-powered airframes for bombers, such as the Horten Ho. 229 and Arado AR 234, the latter of which DID get to see service at the end of the war.