I don't run that particular size radial on my 35, however, I have run radials exclusively on it since the late 70's. There is no way I would ever go back to bias ply tires. In my opinion, fitting radials is the best thing anyone can do to improve the driveability of their old Ford, everything is better, ride comfort, braking, steering, and tire life.
The stock 35 spoke rims will indeed hold air, however, the rims don't have the safety bead that is designed to help hold the tire bead in place, which modern rims have. You can quite concievably run tubeless. Brian