Yes, Italy will remain dependent upon African grain, which will likely mean Constantinople is able to grab Ostrogothic kings by the balls and squeeze when they get uppity. I also agree that at some stage, the largely Greek speaking areas of Italy will probably pass directly into the Byzantine sphere of influence, if nothing else, so Constantinople is able to maintain sea routes with Africa.
The TL I'm writing is yet to be published here. The POD is Justinian and Theodora being overthrown and exiled following the Nika Riots, and being succeeded by one Hypatius, the pleasant, mildly homosexual bachelor nephew of the Emperor Anastasius. ITTL, the conquest of Africa goes ahead as planned, but Hypatius dies of natural causes in 535, shortly after Belisarius returns to Constantinople. Belisarius is then proclaimed Emperor against his will, and rules for forty one years. ITTL, there are Gothic Wars, but they are nothing like as extensive or damaging as OTL, and end up with the Romans retaking parts of Southern Italy, but the North remaining an independent, Ostrogothic allied state.
A map I've done for the TL, in the year 576, can be seen below.