If the ladies are going in shortly before nightfall, I tend to doubt the fertility rate would be all that high. As kikinono suggests, numbers do come into play, but he can only do so much before they go to bed. I've never done it, so I'm not sure how that might effect the flock dynamics either. He may lose his dominance and not perform at all. I don't know about that but it may be a possibility.
You could try it and check the fertility of the eggs after about 3 to 4 weeks. This site gives pictures of fertile eggs.
https://www.backyardchickens.com/forum/viewtopic.php?id=16008
You could trim his spurs to reduce the damage he can do.
You could get some eggs in an incubator and start to raise a replacement rooster now. It's probably earlier than you wanted to raise your replacement layers, but you could get some meat birds this summer or get rid of excess on Craigslist.
You could check Craigslist and probably get a free rooster. This raises some biosecurity issues. You could also advertise on this forum for a rooster, but as much as I respect the members of this forum, you don't know anything about our biosecurity either. And any of us may have flocks harboring diseases we know nothing about despite our best biosecurity measures. Still, people successfully bring in new birds all the time.
You could keep him isolated until you want fertile eggs, then let him roam with the ladies.
Good luck!!
