No; my understanding is you can only use the refillable mug at the hotel you stayed at DURING THAT PARTICULAR STAY (in other words, I cannot bring my refillable mug from our stay at CSR last year and use it this year).
It actually says on the mug: "Refillable only at location purchased; free refills until the end of your stay"
You're not supposed to, but many do. Not advocating it, just stating the facts.