I'm not saying that this wont work, because I've seen examples of many systems that run with a regular gas fired water heater and the owners are happy with them, but to me it just seems counter productive in this application.
The whole idea of floor heat is to heat the slab of concrete to an even temperature before the pump stops putting hot liquid through the tubes in the floor. Once the slab temperature set point is achieved, the slab (assuming it is insulated correctly) should hold that temp for a reasonable amount of time, giving off heat to the room the whole time.
When using a regular water heater. Whenever that slab temp is achieved, and the pump stops, you are now burning up BTU's to keep that tank of water hot until the pump kicks in again. All those BTU's are wasted. With how expensive the overhead is to install these systems, most people try to run them as efficiently as possible. In the OP's case, I guess that doesn't matter much to him, because he bought the house as is.
If it was me, I would collect as much info on how these systems are supposed to run, and do a once over on your current system to make sure everything seems right. If everything checks out I would get a price on installing off peak power vs buy a new gas fired tankless water heater. If it is located in your basement, I would go with a condensing tankless heater because they can be vented with PVC, much similar to the High Efficiency furnaces being installed now days, which gives you more options for installation.
One other thing I would check is if you have a multiple speed pump, and the inlet and outlet temps at the manifold. IIRC, most people try to achieve 120 degree inlet temp, and a 90 degree outlet temp.