I'd give them 8 deep by the start of the tourney:
Past the current starting 5
T Jackson: most likely will be inserted back in starting lineup, but whether it's him or BK starting, his return adds 1
Z Showalter: doesn't even get a lot of mins now, but most times he's comes in he makes some good things happen
D Dukan: He really isn't a half bad player. Sure, he has his limitations, but a couple yrs ago, he'd likely have been a starter for Bucky at this point.
I'm not counting Vito Brown. He seems to play about the same minutes as Zak Showalter, but mostly just looks like he is getting minutes and filling space to me. He may be a future contributor, and these minutes should help in that regard, but not there yet. On other hand, when Zak is in I don't find myself hoping that the stint is brief each time. I find him fun to watch, as he mostly plays like the game isn't too big for him.
I'm not saying they will win a NT. I've watched a couple UK games. I doubt the Badgers could take more than 3 out of 10 against them, and 3 is probably wishful thinking. That said, I think the Badgers have a better chance than last year going in and they nearly were playing for the NT last year. That obviously doesn't mean they'll even do as well as last year, but I think "no chance" is too harsh. UK gets bumped by someone along the way and I see the Badgers as having as legit shot as anyone else.