Unless it's a very correct restoration otherwise, I can't see a 4-synchro box detracting from the value. Besides, you'd have to either drive the car or jack it up to see the difference (if you keep the TR3 gearshift).
There were several different gearsets & mainshafts used during the TR6 run; some of the later ones never came with A-type ODs. You might be able to get a custom shaft made to suit (I believe ORS in the UK can do this). I switched to an earlier TR6 gearset instead.
The OD adapter plate also changed, the early plates won't fit the later boxes without modification (although later plates will fit early boxes). If you're getting a new one, Quantum Mechanics offers a beefed-up plate that is worthwhile IMO (the original ones frequently distort enough to leak oil at the joints).
Otherwise, the conversion is straightforward.
Some indirect issues to be aware of:
Late TR6 boxes had a much thicker front flange. You may need longer bolts & longer studs in the engine block. On my TR3A, I also wound up making a little bracket for the clutch return spring, to get it's length right. Didn't move it to the TR3, now I need to go back and do so.
For TR3/A before TS50k, the later gearbox will hit on the tunnel (the starter bulge is longer). A little quality time with a BFH will solve the problem, but it makes a lot of noise if you leave them touching.
The 4-synchro boxes are about 3/8" longer than the 3-synchro (independant of the increased flange width). Best IMO to elongate the mounting holes in the rear crossmember so the motor mounts aren't strained (otherwise the mounts don't last too long).
It is possible to rebuild the early top cover with the 4-synchro shafts & forks ... I didn't want to lose the dipstick. If you use a later top cover, you may need to drill it out for the cross-bolt used with the TR3 shifter.