I bet they are just comforting themselves. Maddie will suck on my quilt but she gets it wet. Its to bad your rescue does it so often. He probably didn't get enough attention and has just learned the behavior make's him feel good. I can understand it being a bit too much!
I'm with Suzi, I definitely think he is just soothing himself. My old dog (not a Hav) used to lick everything, especially when he was tired. He'd lick the couch, carpet, you name it. It used to be constant for us too and he also didn't come from the best of places before he became ours. I don't think you need to see a specialist about this, it's similar to a human baby pacifying themselves.