yes..... your tranny will bolt up to a 4agze.... you will need to use the clutch/pressure plate/flywheel that goes to that tranny, however...... the E series trannies have a larger input shaft and the C series components won't fit (ie, the clutch won't slide on)... you need to use axles for whatever transmission you use.... if you use your tranny then you need to use your axles.... if you use an E series tranny, you need to use the axles for that....
however, keep in mind that the C series trannies (either c50 or c52) on hard launches tend to have problems at 200whp or so..... along with that, the axles are much smaller.....
also, the E51 tranny is interally the same as the E150 (turbo mr2 tranny) which is nearly bulletproof.... along with that, the axles are almost identical as well.... so you know they will hold a LOT of power w/o work.....
to give you an idea... these are E series axles:
if you don't know what C sereis axles look like.... the input shaft is about 1/2 that size, and the diameter of the axle is much smaller on the C series....
the clutch on an E51/58 has a stepped flywheel.... which is much different than the C series (i really should just go into the garage and get some comparison pictures since i do have a C series axle and clutch/pressure plate floating around the garage)...
notice (if you can see) that the spline is much larger on that clutch.... also, notice the step that flywheel has.... this came out of my e58 and is in my e51......
there is an upside to all of these to using the C series...... it has shorter gearing (better acceleration on the 4agze's) and is almost 1/2 the weight...... you'll probably save 60-70lbs or so going with a C series.....
(btw, side note..... the ring gear diameters are the same on all 4age/4agze's..... so you can use whatever starter you would like, and the mounting is the same..... well, except that some are exhaust side and some are intake side.... but that's beside the point)