Is it true that rimmed and rimless cartridges of the same dimensions can be loaded with the rimless dies (eg 7x57R and rimless, 307 Win and 308 Win)? Thanks!

Generally speaking, yes it is.

I load my 6.5x53R with 6.5 M/S dies, my .356 Winchester with .358 Winchester dies, my 8x57R with 8x57 rimless dies, and several others.

As the part of the case from the base up past the extractor groove or rim, whichever it has, is not in the die but is in the shell holder, the die will not affect that portion.