Yes, but there are probably more of them than there are camera repairers.
Steve.
Digital clocks wiped out most watch repair places in the 1980's. Timex used to have service centres on contract everywhere, then it was mail in, then it was gone. A drugstore chain I worked at many years ago had a Timex-trained technician in most major stores. No longer. Even mid-price mechanical watches are more likely at warranty to be replaced than repaired.
Now it is the very high-end watches that are mechanical and have substantial repair facilities, Rolex etc. The cost to repair is extremely high. They do not do nickle and dime stuff. The employees have to undergo very specific and long-term training in one brand alone. The closest one could come to it is Leica's service. There are watchmaking and repair standards bodies:
http://en.wikipedia.org/wiki/WOSTEP
The thing is, apprentices are trained precisely because there are new watches constantly entering the market, usually at premium (multi-thousand $$$ prices). This assures long-term revenue flow and therefore certainty of investment.
The same cannot be said of cameras. High-end film cameras are still marginally in production, but at lofty prices along with lenses. They simply do not sell on the scale as mechanical watches because watches are seen to have an intrinsic "jewelry" value. They can be seen as ostentatious displays of wealth, prestige, bling, or whatever. Really, only Leica gets in that league. Watches are fashion as much as functional. Cameras don't really have the same investment status as a high=-end mechanical watch.
And watches are not dependent on an input like film. They are, in fact, designed as much as possible, to be completely independent of additional inputs.
There are similarities in cameras and watches as one can see from the presence of Seiko (shutter manufacture especially) in both camera and watch markets. It's no coincidence that cameras and watches have primarily been manufactured in Middle Europe and Japan from companies closely grouped together.
The idea of crossover repair service is quite common. However, the option to repair salvage cameras as a mainline business alongside new, high-end watch servicing does not marry easily. I suspect on the shop floor it is even more difficult to expect a TAG Heuer technician to switch from a $8,000 chronograph repair to a 40 year-old rangefinder cobbling parts from eBay no-sells.
The mechanical watch biz is not faring well. Younger demographics simply don't use or need watches as much due to smartphones and aesthetics. Many do not like the weight on their arms of a watch. That may change, but it is likely to have a secular impact.