These welds are big...but they're symmetric and even. To be safe about the tubing, I don't think I'd be able to totally blend in the welds. (But I've heard that there's a powdercoat capable "Bondo"...) But I think with a Dremel and some time I could turn the welds into a smooth ring around the joint without damaging the tubing.

Luckily the frame was not expensive. If I trash it I can buy another...though Mrs Banzai will be rather upset about that!