I have several different kinds of ajuga scattered in a rock garden at the front of my house. They are in shade and get watering when I do the rest of the rock garden plants that are more in full sun. I walk all over them when I weed or putter around then they look squashed but spring back within an hour or so. I wouldn't worry about planting them in a normal pathway - they will multiply or not depending on whether they like the soil. If they are currently in a place you don't want them to be, what have you got to lose? I also think that if the path gets muddy you need to add several more inches of gravel. You could consider digging a shallow trough along the outer side because if rainwater is standing then you also have a drainage problem.

All in all, I'd say - go for it - the color contrast would be stunning.

I have to watch it to keep it out of the pebble path. It will probably be successful beyond your dreams. My path has 3/4 stone as a base, with pea gravel and stepping stones, so mud is not a problem, but anything beyond a few Ajuga and Violets is not tolerated. Post a photo when you get an effect that satisfies you.