The answer to this really depends on a lot of factors, including that person's goals and how long they stick with it.
If you're looking to become a decent rider, and you can only ride once a week, but you ride once a week rain or shine for a few years, and read up and watch other people ride, I believe you can get there.
Will you be a pro in two years, riding once a week? Probably not.
Not very far depending on your strengths and weaknesses
It doesn't matter how much you ride, it matters about consistently. Before I bought, I only rode once a week and I feel like I've become a ton better
I think it depends on what you do when you ride. Is it lessons or on your own horse?
If you put in the work you can get far.
I had private lesson once a week before I got my horse with an amazing instructor and I improved so much!
I think you'll get what you put in!