The behaviour depends upon when the filehandle is closed. Here's my test :

$ echo "hello" > toto
$ cat toto
hello
$ perl -e 'open F, "<toto"; sleep 30; print <F>'
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At the same time I launch in another terminal:

$ perl -e 'open F, ">toto"; print F 'goodbye'; close F; sleep 30'
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The output in the first shell is "goodbye". If I change the second one liner to rename the file :

perl -e 'open F, ">toto"; system ("mv toto tata"); print F 'goodbye'; 
+close F; sleep 30'
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The output remains goodbye. However, if I change the second one-liner to:

perl -e 'open F, ">toto"; system ("mv toto tata"); print F 'goodbye'; 
+sleep 30'
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So to close the file last, then the first oneliner reads nothing at all.