It is possible. The origins of the wheel lock are not certain. Probably it was German, circa 1480. It may not have originally been a gun: Da Vinci famously included a drawing of the mechanism next to a fire-starting device, so it may have originally been a slick way to light a fire. Complex, yes, but it didn't have to be a clockmaker who produced it: the world of fine metal working was not limited to clocks . If you take look at this 16th c. door lock now in the Seq des Tournelles Museum in Rouen, you will appreciate what kind of work could be done with files, chisels, engravers...this was not the Stone Age..
If you also look at the provenance of 16th c. clocks and wheel lock pistols in museum collections, you will find the same city names mentioned pretty often. Nuremburg notably had thriving population of metal craftsmen, and not surprisingly there are both pistols and clocks being made there in the 16th c. as well as watches,locks, scientific instruments, automatons: the same shop would not likely be producing all of them, but someone who could make springs for a clock or a door lock might easily get a job in another shop making springs for wheel lock pistols. An engraver of scientific instruments might also get work engraving wheel lock lockplates. A supplier of steel for springs or fine wrought iron plate could be selling to all their shops, as could a shop that made and sharpened files. And customers would tend to travel to that city if they wanted some piece of fine metalwork, which drew in more craftsmen wanting to compete. All these things were why craft production in the pre-industrial world would often concentrate into specialties in specific towns.
TL:DR It would have required a fine metalworker to make them, but fine metalworkers were in other trades than clocks and watches.
Torsten Lenk: The Flintlock
I don't think I can say for sure who exactly was producing early wheelocks but it's possible. The gears and spring which spun the wheel were the sort of thing clockmakers would have been already very familiar with. According to Bert Hall, one of the main challenges is the fact that the wheel protrudes into the powder pan, meaning that it requires very fine tolerances, around 0.04-0.08 mm, in order to prevent the fine priming powder from leaking into the gap and clogging up the mechanism. The solution discovered at some point in the early 16th century, Hall says, was to use the hardened steel wheel as a cutter in order to mill it's own slot into the powder pan.
Initially wheellocks were likely just a specialty item made by specific artisans or inventors, which might include people with clockmaking experience. And the mechanism may have originally just been a fancy firestarter like u/bodark43 says.
Curiously, early concerns about the new weapon and the possibility of it being easily hidden on the person of a ne'er-do-well seem to have started spreading much more quickly than the weapon itself did. In 1517 Emperor Maximillian banned both the production and ownership of any "self-igniting hand guns" in hapsburg owned territories and over the next couple decades or so a number of similar laws start popping up elsewhere in the HRE and Italy. It's not entirely clear what happened to most of these laws and how effective they actually were. but they might be part of the reason that wheellocks didn't really start to take off in popularity until the late 1530s-1540s. Once they did though, production costs of the weapon seem to have started dropping dramatically to where in the second half of the 16th century a single wheellock pistol often cost just 12-15 shillings as opposed to up to 20-40 shillings for a full-sized musket (though the cost of frequent repairs and replacement parts for wheellock weapons may have driven up the total cost over time somewhat).
The mid-16th century was also when the snaplock/snaphance first started to appear, which would eventually evolve into the flintlock, though snaphances and flintlocks would continue to be widely considered much less reliable than matchlocks or wheellocks for more than another century. Humphrey Barwick in 1592 suggested that a light cavalryman's arquebus or carbine be made with a snaphance, but not his pistols. Presumably because pistols tended to be used at much closer ranges where you really wouldn't want them to fail.