If you're arriving after noon, there's value in Club Mobay, getting thru immigration (especially if you don't have a private driver waiting for you and you're getting on a large tour bus to get to your hotel, better to wait in the MoBay lounge than the big bus). When I've arrived before noon, I've always gotten thru immigration in minutes (so I wouldn't think there's a need then). As for departure, Club Mobay doesn't help you with the long lines at luggage check-in at your airlines desk (which is, by far the longest wait for departure). After luggage check-in, it's never taken me more than 10 minutes to get thru customs before the departing gate area. Instead of the MoBay Lounge, just go to Margarittaville for some food/drinks and you can use their free wifi (a drink and a sandwich there is usually $20). You can also check the Mobay airport website for arrivals to get a feel for how many planes will be arriving around the time you land.

https://www.mbjairport.com/arrivals