Not really, if anything he had less time. When they found him, it was the end of the school year, so he wouldn't have had all summer to start teaching again. In the Summer, he helped escort Harry to Sirius's house about a month(?) into Summer. I guess he would have had to make lesson plans or whatever over the Summer, but I doubt that's as stressful as doing missions for the order. Though the theory that he's more useful as an Auror than a teacher makes sense too.
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