Aren't northern Sudanese mostly Arab-speaking, if racially varied?
I think so - a "pan-Arab" ideology could also work to unite Egypt and northern Sudan as long as being Arab is defined by language.
If I remember right, Egypt in OTL actually occupied much of the Sudan before it (Egypt) fell under Britain's thumb. For a while, I think, the Sudan was jointly administered by Egypt and Britain. If Egypt could remain fully independent rather than becoming a protectorate, it could have retained the Sudan and maybe expanded even further south and grabbed more territory before Europeans could get there. One big problem Egypt might have had is that without being a British protectorate, they would have been on their own in dealing with the Mahdi's revolt and establishment of a state in the Sudan - assuming the Mahdi wasn't butterflied away by earlier changes.