Can I use AirPlay with an Airport Express when the WAN port is not connected? Is it possible to connect to the Airport Express over WiFi with my MacBook Pro and use it as an AirPlay device when it doesn't have a connection to the internet?

I will not have access to the internet (so no router) for a while in the future, but I wonder if the AirPlay function will keep working.

If this is possible, which of the models support this behaviour?
As long as you can find them with AirPort Utility you will be able to use them as AirPlay device. I've used the same setup and you can wirelessly connect them and they will still function as AirPlay device (they can even make your network more powerful)

Please also check this Apple KB and question with answer on SuperUser 

To make your answer complete: you can do this with both versions.

If you have no internet connected, you will still be able to let the Express function as Accesspoint. You just won't have access to the internet via it, but that's not weird as you don't have an input ;)