I don't think this influences the site's beta statistics. I think the rule is that a question has an "answer" for beta purposes if it has one literal answer with net votes of +1 or more.
Personal thoughts about accepted answers
Personally, I'm not too fussed about whether OPs accept answers or not. Ultimately, I think that votes are a better signal of how well the question has been answered. All too often on Stack Exchange it seems that there will be an accepted answer with say 3 votes, and then the next answer with 20 votes is the better answer, which was posted after the accepted answer.
I also feel that a focus on seeking accepted answers seems to put too much weight on the importance of keeping the OP happy. My overriding concern for the site is that we create great resources that will benefit the whole internet. Whether an answer is accepted or not seems to be unrelated.
I wonder whether it is the nature of this site that often we tackle fairly broad issues where you could write a few paragraphs or you could could write a book. For example, a question about what is the relationship between X and Y might yield an answer that provides a few thoughts along with an example study. This is not really a complete answer, but it is helpful.
Anyway, I realise this is just a personal view, and that it is nice to feel that your answers are appreciated both directly by the OP's acknowledgement and indirectly through the rep bonus received.
How to get feedback from the OP about your answer
I guess comments on the question are one way of getting feedback on your answer from the OP. Obviously, this should be done courteously with a genuine desire for feedback rather than just rep seeking. Just because you've written a reasonable answer doesn't give rise to a right to acceptance.