Do overheard henchmen conversations point towards side quest goals?

There is definitely two kinds of radio-chatter you can hear, during Arkham Knight.

Firstly, as noted in agent86's Answer, there is inane henchman banter. This is generally along the lines of "Oh, [the boss] is a bit of a character, isn't he?" to "I hope the Bat comes here tonight. He's going to be dead soon", and occurs whether or not you have active missions (i.e. flavor text, not useful info).

Secondly, useful content - mentioning the Most Wanted missions (like Gotham on Fire, The Perfect Crime, etc.) These do occur around the area of the mission, and will sometimes cause your mission menu to be updated with Intel (not in the case of the bat-man, unfortunately). I've generally seen this update happen with the Perfect Crime missions.

The vague sort of henchman banter doesn't really lead you anywhere, unfortunately. I still get vague henchman banter even though I've 100%'ed all the side quests and the main quest.

The things to watch out for are:

1. People actively discussing beating someone up - these are the firemen, usually.
2. The GCPD helicopters will sometimes spot side quest locations, and as far as I know, they are always accurate, although the message comes and goes quickly. If you can, open the map and try to set a custom marker in their general direction, so that you can judge the distance/bearing.
3. Hearing opera music indicates a nearby mutilated corpse, but you have to be pretty close.

There are other signs, like the red sentry gun vision cones for the towers, and blinking red lights indicating a mine. The ones I previously listed are the audio cues, though.

If you're having trouble finding side quest locations, don't sweat it - as the main plot progresses, you'll get "intel" about the locations. I believe there are some firemen especially that can't be saved until certain plot conditions are met and you get the intel on their locations.