The important thing in the context of the original question is that mingw uses its own C runtime (MSVCRT is old and incomplete - you would not be able to use it as a drop-in replacement for a modern CRT). You can link the mingw CRT statically or dynamically, and OP suggested that linking it dynamically would reduce the size. But that is only true for the main executable. You would still have to ship the mingw CRT alongside, which in return would increase the distribution size of the program again.
I really didn't want to get into the specifics, because the situation is already complex enough without MSVCRT, but: Yes, it is. If you wanted to do a size-optimzied version of this particular program, it would be a good enough choice.
I hope that clears my point up.