Hi Tim, I did a lesser version of what you're planning a couple of years ago - flew into Kashgar, met a mate, collected a used bike I bought online and cycled down the KKH and on to Chitral. (see this post
If you have read the ACTH book
(like AMH) you may know of the local Flying Pigeon brand, but I suspect a 'ride-to-the-factory' bike like that will not hack a Tibet trip without a lot of 'interruptions'.
Another thing to know is even though many MTBs like Giant are made in China, only the better spec ones (+ Taiwanese) get exported to our rich markets. Locals get lesser spec'd machines with cheapo components. That wont last either across Tibet.
The bike I bought - an ex-rental 'local' Specialized was $200 but only the frame was worth bringing home by the end of that short trip. I brought my own saddle, decent rack, pans and tyres. Local stuff would not have hacked it.
One more thing, AFAIK, the G219 Lhasa-Kashgar road which you would take to get to Pakistan from Tibet requires an expensive escort. Extremely hardcore riders do do it solo, but it requires carrying weeks of food, evading checkpoints at night, wild dogs and of course 4500m+ for weeks.
As Mark says it's great way to go, though unless things have changed, unlike other Pak borders you can get a visa at Sost on the KKH coming in from Tashkurgan (in the mandatory van).
There's the Attabad Lake to deal with too (not prob on a pushbike), but other than that I get a feeling that anywhere in lowland Pakistan, you will be police escorted border-to-border as things currently stand, so make the most of the fabulous northeast; it's another country.
Picture is of a Giant dealer in Kashgar. Plenty on the racks but another thing to consider is that most Chinese are smaller than me at 6' 1", so if you're tallish too, you may find your frame size is not readily in stock or even available. I bought a local bike rented to foreigners.
Me, I would by a quality, little-used MTB here for £3-400, get decent tyres and luggage/rack (another £150) and fly wherever you like. You wont exceed 25kg. The only reason i bought local is that at the time I didn't want to risk my lovely Cannondale in a plane hold. Now I'd throw my trusty (but fully rebuilt) KKH hack on any plane. Just block the forks and remove the discs.
It's all in the ACTH.