I don't know the answer to your question. I've tried to find a straight section of mesquite to use for a bow for a long time. I even cut one piece I thought was reasonably straight but when I split it in half I decided it wasn't straight enough even for me.
I guess you'll have to build a bow to find the answer.
I use mesquite heavily for tip overlays (heartwood) as it is beautiful wood. The borers love it so I'd get it treated with insecticide or debarked and sealed quickly. I'll keep looking for a straight section, at least enough for billets. I'm also watching for a sapling straight enough for a bow, but so far no joy.
Good luck,
George