No its fine, my last house was gravity fed hot water with cylinder, HW only or CH and HW.
Gravity fed works fine (hot water will rise from the boiler to tank and cold water will drop leave the tank to head down to the boiler.
If you want the heating on then it doesn't matter that the hot water is on too, as the cylinder is just a very well insulated radiator. Any heat lost will just help the radiators do their job.
Also, if the tank has a decent amount of insulation and you don't use any hot water, it probably only needs a few minutes top up every few hours so its not a huge gas consumer.
Edit: Even if it was pumped rather than gravity fed, it would make no difference to your shower as it is central heating water being circulated through the cylinder via coil, it wouldn't pressurise the tank (unless the coil was leaking, and thats a different problem) The shower itself is the reason its slow, it can only heat water at a particular rate so has to slow the flow down. Bigger Kw = faster shower, but you would probably need a new bigger cable running to it.