Why shouldn't it?
The religious promotions aren't blessings of active and involved gods, they're techniques developed by those particular religious or cultural groups. If you can make an automaton that can walk and fight, why can't you make one that can walk and fight with those specific techniques? Those techniques are part of how your nation's warriors fight and thus what your automaton's combat style is probably patterned on.
Is that completely unrealistic? Yeah. It isn't any more unrealistic than having a bipedal war automaton in the first place, though.
We have trouble getting bipedal robots to walk
today, much less fight. The clockwork golem is the only one of the -punk units that not only wasn't used historically, but probably
couldn't have been. (Actual clockwork automatons weren't bipedal; the most famous example was a mechanical lion, IIRC.)
Since it's a 100% rule of cool unit already, I don't see any reason not to make it
even cooler by once again allowing it to be a kung fu clockbot.