The 2H is a great engine to begine with and a good rebuild should take care of anything you throw at it. Turboing a 2H will be limited by its high compression ratio and lack of turbo centric internals i.e. pistons, wrist pins, rods, lack of piston skirt cooling etc etc. You could run a turbo on it, say a CT26 with some mods to liven it up at speeds, but you will only be limited to say 7-9 psi of boost if you want your engine to last a while. Also, over heating should be more of a concern with a homegrown 2H turbo since you will be permanently dumping more fuel because of the lack of boost compensation, to cope with more air(due to the turbo), resulting in a hotter explosion.
With the 12H-T, kabuli or not, you should consider that the engine you buy will be atleast 24 years old. So you should rebuild it to high standards and not just worry about the tubro not working anyway. Once you are done with that, you have your pump tuned for injection by a dial gauge, you injector nozzles in order in accordance with the factory manual and the boost compensation set right, with no smoke under light-mild loads and a slight puff when you gun it and the turbo spools, you will have a winner at your hands. I'm sorry for getting a little carried away but 12H-T is just tremendous. Hugely reliable, gobbs of pull and gobbs of go! It will only over heat, like any other engine, if it has a bad cooling circuit, or if you have it over fueled.
Also with a turbo, there is not alot that can go wrong, which you wont even notice being fixed when you get yout whole engine rebuilt. Do the bearings, the oil seal, look for fractures/damage to the turbine blades and housing, make sure it has good fluids supply and that the version of pressure release your system has is working fine.
How much are you paying for the 12H-T?