So if I wired the thermostat to the boiler, every time that the thermostat turns on the heat - would this just heat the water as per usual? In which way would it mess things for me?
Here's what will happen. Then you can make your own decision whether to do it or not.
When the room thermostat is calling for heat, the hot water cylinder will also be heated. When the room thermostat is satisfied, it would turn off the boiler and pump and so the hot water would also go off too.
OK, the hot water will come back on again when the room thermostat calls for heat, so you might get away with it in the winter when the heating is running most of the time. If the weather was mild like now, and someone ran a bath you may have to wait a while for the heating to come on and the hot water cylinder to reheat.
In the summer when the room temperature is 22 degrees, and the thermostat is set at say 21, the radiators will not come on at all, neither will the hot water. If you want hot water you will need to turn up the room thermostat, and of course the radiators will come on too.
OK you could turn off all of the radiators at their manual valves and then turn the room thermostat up, but it's not the right way to do it.
What do you do now in the summer when you only want hot water?