To answer the OP in a rather large nutshell (good topic btw).
No way.
First of all, I have to say it.... The guy was a "balla" in collage. Who wouldn't want him without the injury bug?? However, it's there, staring us in the face as it's doing to many other NFL teams. Normally I would think this could be a smokescreen, but with all that we are hearing, no one is really saying otherwise, we already have more than a couple of questionable players (whether it's injury or retardedness) and the fact technology has gotten much better towards diagnosing these sorts of things I would just stay away.
If we were a team already in contention for playoffs or SB's yearly, I'd say sure why not. But Tampa is not. They are rebuilding still. To bring in a guy like Bowers would be much more of a risk to the Bucs than it would be to teams like Indy, Packers, etc. You get the point. Fact is, Tampa really can't take that chance. To do so would only slow down the team into growing a contender if he does fail. Honestly, I think he'll be gone before TB picks anyway, but if he does somehow slip, I still don't believe Dom will pick him. Heck, I still think Dom would have taken McCoy over Suh if he would have had that chance after hearing about Suh's knees. And I still believe Suh won't last as long in the NFL as McCoy will because of that fact. Suh might not seem like a good player to bring into this argument because he was damn good last season, but Detroit fans still have to wait a couple of seasons before they fall in complete man-love with him.
Imagine if you will. Worse case scenario....
We have Talib (who gets off), but then shoots his mom for putting him through that crap = no top CB for TB.
Then K2 busts knee again = no elite TE.
McCoy falls on his nuts = no high round draft pick at Dline.
Price never heals = without those two, might as well call Hovan. Maybe Mahan? dude is cheap and can't play the offensive side anyway.

Then Bowers has his problem = Back to teen wolf.
You get the point. I actually could elaborate more on that topic, but beating a dead horse isn't all that fun.
So sure, guys like Kerrigan or Houston might not be as flashy as Bowers, but they also don't have the giant red flashing light thingy over their heads either. Tough call, but I would say no. Either you waste a first round overall pick on a (eventual) crippled guy, or a superbowl winner. It's just a way to up and down situation for my liking.