Sounds like a really neat concept.
I'd say you have a few hurdles with this that I'd like to list. They'd have to be addressed in your site and there MAY be some liability concerns involved. Maybe posted as part of a list of rules and etiquette.
1. Obviously the locations have to be in places where it's legal to access and shoot.
2. The targets must have a suitable backstop (or sufficient clear open range) and should be clearly visible as such. For example, it would NOT be a good idea to have a target in a wooded area where the shooter has no idea what lies in the woods beyond...be that domicile, livestock, or hikers.
3. Times for shooting ought to be specified. I'm thinking about "daylight hours only" type. Not only is night shooting a potential problem in some places, there's the safety aspect to think about.
4. Basic maintenance encouraged. Geo Cache people are generally expected to find a given cache and typically leave notes, small knick-knacks, and so forth as part of the fun. You ought to encourage people to assist in this by simple things such as repainting with a shot of spray paint, securing the target in place where feasable, or reporting deficiencies through the website for repairs. (I would not consider it too much effort to carry a can of white/orange spray paint for just this thing.)
5. People ought to be encouraged to "leave nothing but footprints"...remove all spent shell casings, and such. (No beer cans, food litter, damage to environment, blah, blah, blah.)
There isn't much of a liability concern for conventional geo caching activities, what with them typically being a hide-and-seek game with objects and such. But there might be some for target caching. Not being an attorney, I'm not sure what all this would entail.
Maybe this will take off and grow large enough that I'll be able to participate near where I frequent! That'd be neat as heck!