sub is_valid_re {
    eval { qr/$_[0]/ };
    return $@ ? 'NO' : 'YES';
}
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This eval returns a regex or undef, so you could write as follows:

sub is_valid_re { eval { qr/$_[0] } ? 'YES' : 'NO' }
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But I'd _never_ return words when a boolean value is needed. Digits are so much nicer for that. If you want words, you could create yet another sub to turn the truth number into a word.

sub is_valid_re { eval { qr/$_[0] } }
print is_valid_re('abc') ? 'YES' : 'NO';

sub human_bool { shift ? 'YES' : 'NO' }
print human_bool(is_valid_re('abc'));
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