I think block shedding is one of the paramount requirements in a LB. A LB with bad block shedding but good rush moves might could work in a 3-4 as Will (like Aldon Smith) or Sam since those are usually the pass rushers and hopefully they are going against TEs and HB/FB, but may struggle in run support (hard to get off blocks), unless the DL/Jack is good (occupy blocks so the LB can run freely).
In a 4-3, I think he would struggle more since pass rushing isn't a primary need. He would be good on the blitz, even if picked up, but how will he handle getting blocked against the run? It could be something of a mess if an outside run or even an inside run to his gap comes his way, but he's initially blocked by the FB or G (or a T/C depending on how the DL is set and who they can occupy) and the LB can't get off it in time. It would more strain on the safeties and require a very good MLB to come clean up.
I think the LB with bad BSH and good rush moves is a candidate for being a 4-3 DE. Put his hand in the ground and if he doesn't break free against the outside run, that's fine, that's what the OLB is for and the FS/SS can be more aggressive instead of tackling a 5-7 yd gain, he can attack and try to stop the play for a loss. As a pass rusher, his moves will shine and he is that much closer to the QB. Put him on the defensive left (since most RT aren't quite as good as LTs) and let him go to work. Also on the defensive left, the SS is there, who's usually the better tackler/hitter out of the safeties and one of his usual jobs is run support (and in the 46, a set 4-3 personnel can typically handle, he's the 8th man in the box anyway).