That seems to be the case from all I've read about him. And it also seems that he didn't take lessons, but constantly played on everything as a kid- chairs, railings, steps, etc. Art Blakey said he was a disciplinarian. Here's a quote from another Great:
"The greatest soloist I ever heard on drums was Chick Webb. In order to find out where drumming is at today, you must go back to the very beginning. And I think the greatest drummer that ever lived was Chick Webb. He was my favourite drummer. Not that I have too many favourite drummers: Iím not too easily impressed with people. But this man overcame all his difficulties; he was a dwarf, with a big hump on his back.
" -Buddy Rich (in an interview with journalist and singer Les Tomkins)
By the way, here's "My Wild Irish Rose" in its entirety: