Sure, no problem. In fact, I have a TR4 overdrive in my originally non-overdrive TR3 (along with a TR6 main gearbox housing).
Mechanical issues are the same as the non-OD case. For a TR4 box, I believe all that is needed is to slot the holes in the rear crossmember, so the rear mount can be moved back by about 3/8". On my 3A, there was a bent lip on the crossmember that had to be bent down a bit as well. But since the TR4 still had the thin flange on the bellhousing, you won't need to worry about longer bolts & studs or clutch slave mounting.
If you have an early 3A (before TS50001), you'll need to modify the trans tunnel a bit for more clearance around the starter bulge. The early starter will still work, but the later gearbox has a bulge there that the early tunnel rubs on.
Oh yeah, you'll need the longer speedo cable (96" IIRC). It gets routed across the body on the ledge in front of the battery, then curves down the firewall and runs back along the RH frame rail. There's a gap someplace so it can get past the brace. Should be a clamp on the ledge, and ISTR a clip into the frame rail. Then a broad curve under the RH floor and up through the hole in the floor behind the handbrake lever. Mine was rubbing on the floor, so I added a slit length of old fuel line to protect it.
Electrically, you'll need to add the relay and operating switch; and the wires that run to them. Fairly simple, just 6 wires. See the workshop manual for instructions. It only shows one isolator switch, so you'll also need jumpers to wire the second switch in parallel with the first.
I've found it advantageous to add two things not originally in the circuit : An in-line fuse to limit current to the relay and solenoid; plus a diode across the relay contacts to absorb the kickback from the solenoid. The fuse will hopefully keep the solenoid from burning up if it gets stuck somehow, the diode makes the relay contacts last much longer (and allows the use of a cheap modern relay).
PS, if you do have an early 3A, you might want to consider modifying the top cover so you can keep the dipstick functional. I rebuilt my early top cover with the shift rods and forks from a TR6, but I hear you can just drill the boss for the dipstick.
PPS, there's something to be said for adding your commission number to your signature. Makes it easier to answer your question
