I think his stock will somewhat slip similar to what Haloti Ngata and Gabe Watson suffered last year. Watson was a 1st round talent that wound up dropping all the way to Round 4. I don't suspect Branch will slip that far, but more like Ngata. Ngata for most of the season and the beginning of the off-season was cosnidered a sure-fire Top 10 pick. But slipped 5 or so spots on draft day because of his potential weight problems. Branch has similar issues. People love his size now, but once February rolls around and scouts & doctors get to poke and prod him a bit, we'll probably start to hear things like poor shape and potential work ethic ala Jimmy Kennedy. But at least with Ngata, he's playing very well so far as a rookie, something that is rare among DTs.
Branch isn't a bonafide Top 10 pick yet, but I think just from that sort of conventional wisdom, he'll probably be picked somewhere between pick #12 and pick #18 in Round 1...if he decides to come out.
If the Falcons are picking in the 20s, more than likely the DTs we will have to target are:
Quinn Pitcock, Ohio State
Frank Okam, Texas (Junior)
Tank Tyler, N.C. State
Brandon Mebane, Cal
Justin Harrell, Tennessee
There are others, but mostly they're juniors that may or may not come out like FSU's Fluellen and LSU's Dorsey. But both Mebane and Harrell need to step up because most are giving them 2nd round grades now.