To answer the question from the OP, I think UMass has the best chance to advance...They have the size to matchup with BCS teams and can score in a variety of ways. If they can get past round 1, and they should, I like them to knock off Duke. Putney's length/athleticism is about the best you can hope for in dealing with Jabari and I think Chaz will get in the lane at will against Quinn Cook.
I'm a doubter on UVA, so if GW gets past Memphis, I wouldn't be shocked to see them take UVA out. GW is pretty good in the half court and I could see Creek and Garino knocking down shots to pull out a close one...I picked UVA to win (and then exit to Mich St), but wouldn't surprise me.
vcu should be fine against Stone Cold Steve Austin, but I think UCLA is a terrible matchup for them. UCLA is top 5 in assists and A/TO ratio and having a 6'8 ballhander in Kyle Anderson will help in terms of breaking the press and allowing them to go small (which they like to do) and get good looks off the press break for LaVine, Adams and Alford's kid.
I don't see SLU, UD or St Joe's getting past round 1 (although I guess it's called round 2).