Greetings from a fellow Tri Railer.
Assuming you are on time. Yes, IMO you should make the 620P train, however this all sounds very tight. Especially since the Tri Rail doesnt go to the FLL airport itself. You have to get on a bus from FLL Airport station to take you to the airport. That can take upwards of 15 to 20 mins extra. And do you have TSA? Does Alegiant participate in TSA? If not, you run the risk of long lines at FLL, and Feb is high season in FLL.