It might.
Check with whomever administers that machine to verify the sendmail installation is probably the best starting point. That'll tell you if the path exists. Will your script work? who knows? :-)

Also, you may wish to investigate the $^O variable :

my $mailprog;
if (lc($^O) eq "mswin32")
    #here is winland. 
    {$mailprog = 'C:\sendmail\sendmail.exe'} 
    # or whatever. I don't use sendmail on windows.
else
    #here is *nixland
    {$mailprog = "/usr/lib/sendmail"}
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Update : Duh. Fixed error thanks to chromatic.