I say this in levity, but also half seriously, if only because many times it has almost seemed as if a fighter literally responded to something said by an announcer. Examples: Ali-Lyle: "...he can't really go the place anymore. OH YES HE CAN!!!" Tyson-Botha: "That's the mark of a shot fighter when he can't get off punches...[thunderbolt strikes]" Foreman-Rodriguez: "With Foreman we are talking about a man who has been known to knock out opponents with glancing blows. What becomes a knockout punch doesn't always look like one AND RODRIGUEZ GOES DOWN!!" Foreman-Cooney (doesn't quite fit the theme but included because it's funny): "Now he's got a minute and eight seconds left; let's see if he's learned anything about how to survi- THIS FIGHT'S OVER!! THIS FIGHT'S OVER!"
I have personally heard commentators tell another commentator: ""I think he heard you since he's now going downstairs!". Think it was Teddy Atlas involved. So it does seem that commentators can indeed be overheard. In fact, sometimes fighters say things to commentators when they get close to where they are sitting and interject relevant comments into a conversation they are overhearing.
I am sure in many cases it can be heard. I noticed in Japan when Tyson fought Tubbs, you heard the punches landing. it was quiet, and on an undercard once, Hearns fought Maynard, and you could hear Hearns grunting when he threw punches. I never knew he grunted until I saw that, since usually he fought the main events and it was loud.. This was when many of the seats were still not occupied and it was quiet, so if you can hear him grunt, I bet the announcers can be heard. in that situation.
My personal favourite is Harry Carpenter's commentary on Ali-Foreman: "Ali looking very tired now... in fact he looks like he can hardly keep his arms up... oh, he's got him with a right hand!"
Ali always seemed to have a really keen awareness about his standing during a fight. He seemed to know exactly when he was losing a round, or when he hadn't landed a punch in a while to keep the fans entertained and the judges happy. I wouldn't be surprised if he was ribbing off of what he heard at ringside. We all know that Floyd could hear the commentators.
Also to add, it must depend on the fighter. When I first sparred, all background noise was blurred out. I could hear things, but I couldn't listen. Only after some experience could I listen to instructions during the heat of the sparring. So I imagine to hear the ringside announcers among the crowd noise of tens of thousands of fans, and under the bright lights, it takes some exceptional composure.