How much of the old bike do you plan to use? Some MTB rims are a bit wide for proper road tires, although you can usually get away with it. Gearing should be pretty good, especially for hilly tours, if you don't want to change anything there.
Does the frame have mounting points for racks?
It's useful for a tourer to have some off-road ability, at least in the UK, because some of our cyclepaths are basically tracks, so you could end up with the perfect bike.
Different bars might mean different levers, and so on, but it's surprising what you can get away with ... I once took an undersize (youth size) road bike and made it into a kind of hybrid-mtb with solid 26" tires, straight bars from a child's bmx, a longer seat post and not much else. Best part was it was worthless, so I didn't care how I abused it!
It was stolen from our back garden (yard), so I have no idea how long it would have lasted. I suspect the old frame might have broken with serious off-roading, but it was fun on trails and tracks. Brakes were rubbish, mind you
But starting with a good frame you should end up with a very good bike.
Roy
PS. The only drawback is you could spend as much on parts as you would on a new bike, unless you can re-use more than just the frame.