I don't know about a 340 Utility, but on my 300 Utility the torque amplifier is basically a manually operated underdrive unit. It gives a lower gear corresponding to each "regular" gear, including reverse. When engaged, it also acts as an overrunning clutch or sprag-type mechanism that allows the tractor to "freewheel" so the engine will not brake the tractor. (Careful!)
The tractor drives just fine without the T.A. (just leave it disengaged). Of course, you won't get the benefit of the increased torque at the rear wheels, but that may not be important for what you want to do with the tractor.
Every manual I've seen dictates a tractor split in order to fix the T.A. You can draw your own conclusions about difficulty and expense.
The T.A. is one of two Achilles' heels on the 300 Utility; the other one is the underdesigned steering box. There are some upgrades available to beef up the T.A. One involves oversized balls for the ramps, and the other involves replacing the assembly with a sprag mechanism. You can check the archives on this site to find out more about these options.
The T.A. on my tractor--and most likely on yours--is entirely mechanical; no hydraulics.
I hope this helps!