Personally I think a thumbless grip is suicidal, however someone mentioned at the begginning of this post you may feel it more in the tri's that is the case for me when I do JM presses or close grip bench I actually feel it more in my tri's. But I bench with my thumb locked around.
Although when you thiink of it, if you have a nice amount of weight on and the bar takes an odd roll towards your thumb there is only so much weight your thumb can hold.
BUt I'm still a soft beginner with a miniscule 345 bench.
Natural,
Mike