The round tube, even if welded at the ends, won't be substantially loaded until it contacts the square tube in three places, e.g. after the square tube has buckled. Then, yes, it will help resist further deformation, but it's still a very small tube for use in a rollcage. I'd use the .120 wall, thicker if I could get it and fabricate it, larger in diameter if I could possibly squeeze it in.
I'd also take a serious look at stuffing the A-pillar with hardwood, e.g. oak or ash, instead of the steel tube, completely filling it and gluing the wood in for good measure. That would keep the pillar from buckling right away, and stiffen it up a bit.
Actual detailed analysis of either case would be a nightmare absent modern tools, which I don't have and probably couldn't use if I did.
If you want to be a little scientific about it, build a couple of analogs of the A-pillar, reinforce them in a couple of different ways, then fit a pressure gage to a hydraulic press and measure the force required to deflect the analog, say as a centrally loaded beam, keep going until it stops looking like an A-pillar, and integrate the forces over the total deflection to get a measure of the energy absorbed.
Mike Halloran
Pembroke Pines, FL, USA