This might not be a bad way to go if you are the only one who ever uses this script. But I'd think a series of splits combined with a clear "if" rather than the embedded ? will make the code a lot clearer and perhaps execute more quickly.

my $time_stamp = "2-19-01 3:22 PM";
my($date, $time, $am_pm) = split(/ /, $time_stamp);
my($month, $day, $short_year) = split(/-/, $date);
my($hours, $min) = split(/:/, $time);
if ($am_pm =~ /pm/i) {
    $hours += 12;
}
my $year = 2000 + short_year;
my $sql_time_stamp = "$year-$month-$day $hours:$min"
[download]

I know this looks a lot more like "baby talk Perl", but ask yourself which one you can read more easily without background info. Also ask yourself which one is easier to change if your date format (into or out of this function) ever changes.