I went fourth round, but it would have to be the right team even then.
Every team has major needs (left tackle, center, linebackers that can stop the run and cover down field, a shut down corner, etc)....there are just too many actual needs to waste a pick on someone you hope you can find a spot for just because he's a good kid.
And unless you're Tampa, Atlanta, or Miami (and maybe Carolina), you couldn't draft him just for his name. NFL fans are a different type for the most part. There isn't a ton of carry over from die-hard (read: money spending) NFL fans into college football. Typically people follow and spend money on one (NFL or CFB) and are a casual fan of the other. Tebow-mania wouldn't last past draft day for fans in Kansas City or Pittsburgh or Cleveland, and thus, your investment better be for football reasons, not marketing reasons.
It's way too early to ask this question. If you had asked this question about Matt Jones before the combine, he would have been nearly undraftable. But after watching him work out as a receiver, he made some believers of GMs. We'll have to wait and see if Tebow goes all out as a QB or if he works some as TE or something. I think people already assume he could be a fullback. But how high do you draft a fullback that may or may not get 10 carries? Jacob Hester and Heath Evans were both 3rd round picks and were known commodities at FB.
Assuming Tebow could be a FB has to drop him at least one round past those guys.