Bill Connelly breaks down the Knile Davis situation at Arkansas in regards to whether he should or shouldn't play. You should read it, because it goes into far more detail than I do here. Davis is getting close to being able to participate despite having broken his ankle in August.
I think that Davis should be allowed to make the choice if doctors do clear him to play. He would burn his 2011 redshirt, but that only matters if he's not going pro after 2012 (and he's likely gone if he stays healthy). Only another catastrophic injury would keep him around for a fifth year, and unless the timing is particularly bad, presumably that injury would be enough to earn him another shot at a redshirt.
Yes, playing Davis could help the Hogs against LSU, but they're really held back by their loss to Bama. If they do beat the Tigers, they'd have to be more than five spots ahead of the Tide in order to play for the SEC title. Unless the same Auburn team that just lost to Georgia 45-7 pulls off a titanic upset, the Razorbacks aren't going to play for a championship of any kind. It's true you never quite know for sure with the BCS formula, but voters will almost certainly vote Bama over Arkansas. Plus, an Alabama-Arkansas rematch would be less palatable to them than, say, a Bama-LSU rematch if all hell breaks loose.
Playing Davis would be a calculated risk, but the team would need a lot of help to make it truly worth it. That's why I think Davis should be the one to make the call.