I'm not a expert, but from what I read in my Lyman Manual, 49th edition, I would say no.
Let me quote the last three sentences which talks about ammo not reloading ...
"Never put a 375 Winchester round into a 38-55 Winchester. Nor should you
attempt to use 38-55 ammo in the 375 Winchester. Incompatible neck diameters
can cause serious hazard.
According to the diagrams in the manual there are some small differences in case diameters
and a somewhat bigger difference in the neck diameter. Since it's a rimmed case it going to
head space off the rim so the difference in case length may not matter.
I'll wait and see what others say