Yes, it's possible on some systems (assuming the Perl file handle is associated with a system file handle). For example, the following works on (some?) Linux systems:

$ perl -e'
   open(my $fh, "<", "/etc/passwd") or die $!;

   my $fileno = fileno($fh);
   defined($fileno) or die "Not a file handle";
   $fileno >= 0 or die "Not system file handle";
   my $qfn = readlink("/proc/$$/fd/$fileno") or die $!;

   CORE::say $qfn;
'
/etc/passwd
[download]

It would be better if your program tracked this itself, though.

Note that Perl provides $ARGV when reading from ARGV (e.g. using <>).