"I wonder what will happen if I try to tee(append) directly to the file without closing the perl file handle for that file. Intuition tells me I shouldn't..."

Perhaps worthy of a test, but I'd go with your instinct here. You may introduce an issue in code that may work now, but when it goes awry later, you may be scratching your head as to wtf is happening... "it worked before!".

I've never tried it to be honest, but doing things manually outside of an open file handle just can't be good :)