The answer to your headline question is yes, coal seams in the blue mountains are burning. But that has been the case for the last 6000 years or so as Mt Wingen (Burning Mountain) at the north end of the Blue Mountains has coal seams that have been continuously burning for that long. There are others which seem to have been burning at least since the sixties, and every bushfire season, exposed coal seams are at risk of igniting, so it's not a surprise.
Specifically for this current crisis, there are reports via various Australian local media that there have been ignition points in coal seams near/in Lithgow, for example:
The Mercury Lithgow from 4 Jan 2020:
24liveblog from 11 Jan 2020: