The documentation for require does specify that *.pmc takes priority over *.pm files.

Before require looks for a .pm extension, it will first look for a similar filename with a .pmc extension. If this file is found, it will be loaded in place of any file ending in a .pm extension. This applies to both the explicit require "Foo/Bar.pm"; form and the require Foo::Bar; form.

The documentation for use doesn't seem to mention *.pmc files.

Why would one want to pre-compile the code to include?
My guess is that it gives better performance as the code doesn't need compiling when the script is executed and/or that it provides better security as it is significantly more difficult to look at compiled code and work out what it is doing and how...