I could see them drafting a running back on day 3, but that'd likely be the earliest. Who knows when Hill will be back and for a team that wants to run the football as part of their core scheme, you don't want to get caught short. If they think Hill will be ready, between him and Patrick Taylor they have enough depth, so it's not a priority and they can either draft one late or grab an UDFA.
If they use a draft pick on a RB that's fine. As it stand right now, they have 7 picks. They likely get 2 compensatory picks for Linsley and JWilliams (a 4th and 6th?) which puts them at 9. If they trade Rodgers that'll likely net them another couple. They've got plenty of picks, so using one on a RB isn't a big deal if you get a quality player.
As for Braelon Allen in 2024, I don't see him as a Rd1 type guy unless he really does some special things in the next 2 years and at the combine. He looks a little like AJ Dillon and so seems more like a day 2 guy at best.