This is interesting !

So from 3:20 to 4:45 you have 1:25, and the -minimum- transit time (on board the trains) is 43 minutes. However you must consider the time spent getting to the mtr and getting to the platform, the time it takes for the train to arrive, the long-ish connection between Central Station and the Airport Express, and the time it takes for the Airport express train to depart, which can be as long as 12 minutes.

In order to use the in town check in you would need to arrive to the counter 90 minutes before departure which means you have to be at the airport express station at 4:00pm.

It doesn't sound impossible, but it sounds like you have a very real possibility of not making the flight if things aren't 100% perfect. You could also take the MTR to Yau Ma Tei and then ride hop on a taxi to Kowloon Station to catch the express, but it also sounds risky.

The best idea would be to leave class around 20 minutes early, otherwise you are flirting with disaster !