Depending on what grit the stone is, it could certainly work - does the knife(s) get sharp enough for your uses?
Not sure what your definition of inexpensive is, but I have found the Spyderco Sharpmaker is a super simple and effective way to get all my knives sharp. It may be a bit pricier than other alternatives, but it's so foolproof that I end up sharpening and therefore keeping my knives razor sharp at all times.