The closed system works on pressure, if you open a faucet you will lose the pressure and the system will not work. Also, a hot water heater might have a recovery problem depending on how many feet of tubing you have, the R value of insulation and what powers the hot water heater. If you are planning electric there is a good chance it will not work, the heater will not recover fast enough.
I tried an electric tank heater in my previous building and ended up converting to a gas fired unit. My new building has excellent insulation, 1,800 feet of pex in five loops, one zone and is pushed by an on demand gas wall mounted hot water heater, it works very well. I heat the “water” to 110 degrees and keep the thermostat set at 60 degrees year round.