Im pretty sure they also sold a carabiner to do exactly what you're planning, so yeah as long as they didn't engineer their mugs to only fit *their* carabiner then you should be fine. 

Welp, I'm relegated to the Diet sodas now (Stupid Deebs 2), but Awwwwww Yeaahhhh!!!!!!! Honestly, my WB Mug is my fave go-to at home, though one of my kitties also loves it, and she drools... (I recently picked up a set of Korean metal rice bowls, and the lids fit snugly over the mig, so drool averted).