I admire this question! Unfortunately, most songs including their titles are like poetry. This means that they don't follow grammar rules most of the time :)
Even "Love me do" is such a strange combination of words that Love, Me Do and Love Me, Do have completely different meanings. Love, Me Do could be read like, "Sincerely, Me Do" which is odd. And Love Me, Do could be read as, "please love me, Do". No one is named "Do"... Soo this is also odd.
Sooo.... No. maybe no comma needed.. Maybe?