I seriously doubt if comparing to \*STDOUT will do. After all, a filehandle is a special entry in a typeglob, it's not just a plain scalar that you can compare. It's not even a reference.
But you can always use fileno, and applying the snippet of code on the page, you can do:
And yes, fileno(STDOUT) is allowed by strict.
There could be a bit of a problem if $fh is a tied filehandle instead of a physical handle. In that case, fileno will return -1, which is different from the default value for STDOUT, which is 1. If you tie STDOUT too, then you're in trouble.