Yes. We used to do it all the time until Air Jamaica canceled their service from Miami. It was a 7:05am flight to Kingston, a 25 minute layover, and then a 20 minute flight Montego Bay. We were on the beach at CSA by 10am.
My brother and sister-in-law are doing this in 11 days. They are flying out of Fort Lauderdale with a layover in Kingston and still arriving in Montego Bay at 10:30 AM with Air Jamaica. We arrive from Charlotte at 10:54 and will meet up at Couples airport lounge (provided both flights are are on time) and still have a full day at CSA. What a way to not spend your first day of vacation on travelling.
We are taking the Fort Lauderdale to MJB via Kingston as well since it was the best option to get in early. Since you don't change planes the chance of losing luggage in Kingston seem to be remote, I hope!