Yes definitely monitor the cough, there are so many reasons it could be happening. Most of the time it's nothing to worry about, just natural.
Kai stepped in liquid detergent and licked his paw and got VERY ill for about a day. After 3 days he was back to 100% but he has a cough leftover. The vet says certain chemicals like liquid detergent burn and most of the time they dont make your cat as sick as Kai got, but they will hurt the throat and tummy and cause a bad cough for a week or so.
The reason I bring up my situation is Kai only coughs when he eats or drinks because it hurts his throat as it is healing.
Mind you, it is more likely your kitty just has a hairball or something stuck in his throat. Or perhaps he ate a toy (EEK!!). Or maybe he's just trying to clear his throat to get your attention :) lol. Like I said, there are so many possible causes that its hard to tell! Just make sure you monitor and if it persists or seems to get worse I would bring him for a checkup to the vet. That never hurts (except your wallet).
Good luck