Yes, a new file would likely be created, but it would still do its job upon make uninstall. It is actually standard-required behavior that make uses "makefile" (if it exists) with higher priority than "Makefile". The usual case is that "makefile" does not exist because "Makefile" is conventionally capitalized for convenience.

even package managers will still put stuff in random places like binaries outside my $PATH.. or not even clearly telling me what the binary is named or how to execute what I just installed.