Probably not, since this story is likely a fairy tale, but I'm sure some of them do recall that the Mongols adopted Islam not long after. Btw, Hulagu sacked Baghdad in 1258, not 1259.
How could you read Damascus....and then confuse it with Baghdad.
That you are ignorant of history is your failing but I aim to correct that.
And he sacked Damascus in 1260, not 1259.