The vacuum advance units on the 45D type distributors can be replaced with the unit in the car, but it makes life difficult. Especially depending on what position the advance unit was set in when the distributor was installed and if your car still has its AIR pump and emission control gear in place.
There are small screws holding the unit to the distro body that go in sideways and the whole sliding plate and other internal assemblies that have to be removed and reassembled to connect it. Many small screws and things that might fall into the works and be lost.
Also, there could be reasons for the failure beyond the diaphragm. Make sure you check that the sliding plate has not seized, broken or is otherwise stuck in one position. Also that the upper and lower shafts are not worn and the weights and springs are intact and functioning properly. While you would definitely have to reset the timing on removing and reinstalling the unit (which would be a good idea and probably necessary anyway even if just replacing the advance unit), removing the distributor gives you an opportunity to properly clean and inspect the workings.
My advice would be to photograph or otherwise mark the advance unit position and wiring so you can reinstall it fairly close to where it came from and take it out to bench inspect and repair it.
Just another note: You already ordered the advance unit. Lucas distributors for MGB's are completely interchangeable as complete units. Any of them will fit the engines and drive from 62-80. Most MG's, for reasons you are now beginning to see, do not have their original distributor anymore. Early 45DE "Opus" units, as your car should have, were notoriously bad and most have been replaced either with the earlier point-type models, later CEI units or aftermarket conversions. You mentioned you have a CEI distributor. Someone might have installed one on your car, but the advance units for the various 45DM (CEI) units are all different. If you have not already, you might have to check the distributor's Lucas part number to be sure what you ordered is correct.
I hope that helps you. Good luck.
Art