Hi!
So at the simplest level you could use one of our ticketing solutions like WooCommerce Tickets and simply create two different tickets – Members and Guests – for each event and verify if they are truly members at the door.
If you need something a little more involved and members have logins for your site (or you can generate logins for them) you could implement a fairly simple customization to hide the Members ticket from those users who aren’t logged in and vice versa.
That to say, what you want to achieve is completely possible: how in depth this needs to be will dictate whether or not you need to make a customization or use an additional members plugin – but in principle it sounds like you could get everything up and running with just The Events Calendar (our free, core plugin), WooCommerce Tickets and WooCommerce itself (also free).
I hope that answers your questions, but please let me know if I can help with anything else 🙂