are you asking about a "naked " bullet or a lubed or patched one?
No. Paper-patched.
My understanding is that the velocity limitations of the paper-patched bullet are not due to leading the bore (as naked cast bullets do) but due to either spinning apart or atmospheric friction.
I've read that a paper-patched pure lead bullet can't go much past 2200 fps. If you push it above that, you need to harden the lead, again not for internal ballistic reasons, but external ballistic reasons. I thought that perhaps the 2200 fps figure was derived from experience with a .30 caliber weapon. Typically .30 twists are 1:9" give or take an inch.
So maybe you could drive a pure-lead, paper-patched .35 Whelen to say, 2400 fps, whereas a pure-lead, paper-patched .30-06 would be limited to 2200 fps.
If the velocity limit is due to atmospheric friction, then caliber won't make a difference, although perhaps B.C. would. It doesn't appear that the atmospheric friction would be the cause of problems with pure lead projectiles. Lead exposed copper jacketed bullets can be shot at very high velocities.
Actually, I think Dead Center makes some non-jacketed muzzle loader bullets that are intended to be shot at 2600+fps.