If you run that on its own then I would expect you will get no output at all because you don't print anything anywhere inside the loop. Perhaps what you want is:

while (<>){
      if (/^#!/){
        $_ .= "Add this line.\n";
  }
  print;
}
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perl -i.orig -p -e 's/^(#!.+)$/$1Add this line/' file
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To expand a little bit, the -p flag tells perl to wrap the whole script inside a:

whie (<>)
{
  # ... your code
  print $_;
}
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The -i.orig tells it to first rename the original input file to its old name followed by .orig, then run the script and put its output into a new file with the same name as the input file.

I suspect the code snippet you started off with assumed you were running under perl -p.

If you invoked the script in some manner similar to:

The first thing that will happen is that the shell will erase the file (or move the end of file marker to the beginning of the file, which is kind of the same thing)

Also, as noted by our beloved GrandFather and johnnywang your script isn't generating any output

corrected homenode links