Yes, generally....
.45 ACP bullets run .451/.452 in diameter. Current .45 Colt bullet are about the same, but guns made before WWII generally use a diameter of .454 for the .45 Colt, and some older bullet designs may be sized for the older standard.
Also, the expander in the .45 Colt die set should be checked. If it is too large, the .45 ACP bullets will be a loose fit, which can give trouble.
Some .45 ACP bullets have a crimping groove (cannelure), many do not. Most .45 Colt dies will roll crimp, which should not be used with bullets without a cannelure. To crimp bullets with no cannelure, a taper crimp must be used. Normally this will require the use of a seperate crimp die.
If you don't crimp your .45 Colt ammo (no matter which bullet), you can have problems with bullets jumping forward due to recoil. A tight bullet/case fit, and a good crimp will keep the bullets in place, even with heavy loads.