It depends on what your goal is. If you want to be a fighter . . . then no . . . you will need to train a LOT more than once per week. If you are doing it just to learn and have fun with it, then once per week along with "self training" is just fine.
MMA is fun. But . . . it is a ton of work if you plan to be good at it. You can't just pick it up overnight. It takes years to even get decent in all areas. If financial means is a roadblock, start with videos and such. Just learn AND PRACTICE the basics over and over. This will give you "the bug" to get better. Then . . . take it from there.
Good luck either way!