Good question and my gut feel is no, it's not a good idea unless you find some way to mix the water even if you don't do it using the regular pump. Perhaps using some sort of submersible pump temporarily after adding the chlorine might mix it up somewhat if the pool is small and you point the outlet hose in a way that tends to swirl the water (especially for a round pool).

Closing late and opening early is probably your best bet. Some people close with a strong dose of Polyquat 60 in addition to chlorine. If the water is cold enough, the Polyquat will last quite a while. Even chlorine will last if not exposed to sunlight. In my own pool with a mostly opaque cover and with the water at 50ºF during the winter, my daily chlorine loss is around 0.1 ppm FC, but I'm able to maintain the chlorine level adding some every couple of weeks.