Chad really should have joined in Somalia's place. And you are correct. Chadian Arabs are very much a cultural extension of the Arabized Nubians/Cushites of Sudan. They even use the same mat-tents Somali nomads do and histrorically dressed in
the white tobes our ancestors and those of various Ethiopians, Xabashis included, used to:
Baqqara Arabs, who are quite predominant in Chad are also quite common in Sudan. And the cool thing about those chaps is that they were historically cattle pastoralists who also rode their cattle (hence the name "Baqqara") which seems to be a very ancient Cushitic practice depicted even in cave paintings in Somalia:
A Rizeighat horseman (Chadian Arabic speakers):
Compare him to these charging horsemen all the way in what is now Puntland around the same time period:
Waa our kin.