The stock bore on the B20 is 84mm. Generally the assorted heads that come off 81mm bore motors don't need the chambers deshrouded to work on a B20 block, there's enough tolerance in the machining that the extra 3mm doesn't tend to present a problem. The stock B20 pistons are crap and should be gotten rid of ASAP. Factual details aside, it is still more advantageous to take the LS block you already have and get new sleeves like Golden Eagle or Darton installed and bored to 84mm which will give you identical displacement to a B20.

Practically speaking however, the stock LS block can take plenty of abuse. Beef up the rods and pistons and it'll take enough boost to get you very quick. Only problem with the whole running 12's idea is that it just ain't gonna happen on street tires. When you make enough power to pull that kind of ET, the traction of non-slicks is overcome relatively easily. You'll have a great trap speed but your 60-ft time will suck. If you turn down the boost to get the tires to hook up, you won't break 12's. At the very least you need a set of drag radials.