Absolutely yes! I have used vegetable broth, beef, pork, chicken, and turkey before. Each one of them imparts it's own unique flavor to the potatoes.
Beef course is more robust, so you should use it when serving beef or lamb or even a game meat. Cut back on the salt used in preparation.
As mimind pointed out the kitchen is a great place to experiment with food. I do it all the time, some successful, some had to go to the rubbish bin, but we then lean from those mistakes and move on.