But not sure if the coating is sufficient protection like standard romex.

I have ideas on this fireplace, since I cant demolish it (for now) I think a coat of paint is in order.What do you think?

Clear coating them would probably be sufficient.

Then prime with a special paint and then do the final regular coat.

oh and get extra paint  I  am sure  you will need a couple coats. 

They used globs of construction adhesive to make them stick better and then spread a liberal coat of polyurethane on them!

Too many variables to give a definite "Y or N" answer but as it appears we are in similar boat, I'll give my 2¢.Different animals when looking at house-hacking a MF in CA or purchasing out of state.

I occasionally do this with rentals but we are talking about prior to a coat of paint and rug cleaning.

Then, as Brian suggested, you should rough up the clear top coat with sandpaper.

Then you will need to top coat that with whatever color/s you may go with.