Yes. In fact it even simplifies the code, and you can use the Core Time::Piece module:

use warnings;
use strict;
use Time::Piece     qw();
use Time::Seconds   qw(ONE_DAY);

my $t = Time::Piece->new();
my $past = $t - (60 * ONE_DAY);
while (<DATA>) {
    chomp;
    if (/\d{2}\d{2}\d{4}/) {
        my $dir_date = Time::Piece->strptime($_, '%m%d%Y');
        print "delete $_\n" if $past > $dir_date;
    }
}

__DATA__
11012014
11132014
10092014
09092014
11112015
01012015
04012015
01042011
10122014
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