Opinions are sharply divided over whether a word rhymes with itself (it's as futile as arguing whether 1 is a prime number or not).
IMHO it does not, it is the height of laziness and defeats the whole object of poetry/rhymes. A really crass example of this is The Gambler by Kenny Rogers. OK, OK, it's taken me forty years to notice.
From azlyrics.com:
Verse one
On a warm summer's evening, on a train bound for nowhere
I met up with a gambler, we were both too tired to sleep
Verse five (or is it a chorus? There's barely a difference):
'Cause every hand's a winner, and every hand's a loser,
And the best that you can hope for is to die in your sleep.
Verse six
And when he finished speakin', he turned back toward the window
Crushed out his cigarette and faded off to sleep