It can be done, a coach waiting until after the playoffs. There is one guy that comes to mind and its none other than Lannings's Boss Kirby Smart.
Kirby was named the Georgia HC right after the SEC Title Game in 2015, he stayed on as Bama DC thru the playoffs while also juggling recruiting duties for Georgia. Its not an easy thing to do but it can be done. And Kirby could give him some pointers on how he was able to do it. In 2017 Kirby won the SEC and had Georgia in the Playoffs but lost to Bama 26-23 in the title game.
But then again this Portal thing wasn't around back then I don't think. The Portal though also works both ways and the new HC might be able to use it as an advantage.
Props to the Mrs. for reminding me of this yesterday.