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"}
Update : Duh. Fixed error thanks to
chromatic.