One might expect that to be the case, but no, the arc doesnt behave that way (it does when there is no salt though).
My guess, and I had this theory before i tried the experiment so it partly proves me right, is that the conductivity of the salt in molten form would prevent that from happening. The plasma stays inside the hollow chamber surrounded by the liquid salt which helps channel it. It never rises due to an electrically conductive physical barrier.