Monoblock tap - check valve?

I wondered if the hot water would get into the cold when cold taps were open. Would that reduce the pressure enough? Would it be a problem if it did?

It is possible but only in the event of loss of pressure on the mains due to a fault or maintenance. It's the reason there is a check valve in the cold feed too, the water authorities don't want potentially contaminated water from your hot water system being sooked back into the mains in the event of a pressure drop.

Back feeding of cold into a gravity fed hot water system is an issue on mixer showers without check valves or where a hose is fitted to a mixer tap and both hot and cold are turned on. Could result in loss off H/W temperature and ultimately overflowing of H/W header tank.