I live in a block of flats where cold water is gravity fed from a
large, shared water tank on the roof (about 20 ft above). I want to
install a pump to provide a high-pressure shower, but all installation
guides I've read insist on an independent cold feed from the tank to
the pump, which I can't provide.

It will work without a separate feed. The main concern is actually that
you'll "steal" the water from others sharing your tank if they don't have
independent feeds from you, which may be antisocial (or even against your
lease terms). If everyone has their own pipe back to the tank, it won't
matter, unless the tank is undersized.

You should have the check valves anyway if it is a shared supply.

Christian.