Will there come a time when the rift valleys in East Africa become large narrow seas?

Assuming nothing unforeseen happens and the tectonic plates keep moving the Great African Rift will continue to split the continent apart and a new sea will be formed.

presumably. and what would happen is that a new microcontinent would form at the expense of the continent of Africa. Somewhat like India and Madagascar did at one point, say.

Rifts do fail though. It may be that the East African Rift will fail, cease to expand, leaving a deep crustal weakness in that part of Africa. There are many such failed rifts around the world and some are still regions of unusually elevated seismic activity now despite dating from hundreds of millions of years ago.