Hi Bryn,
Sure, like any other app this should be possible yes, but you might discover some difficulties when framing on your way which isn't Mendix specific. There is some experience on the forum already, specific from Enzo, with specific framing Mendix into Wordpress. Maybe you could re-use some of the knowledge of these topics:
https://forum.mendix.com/link/questions/19342
https://forum.mendix.com/link/questions/18882
In general if you want communicate to your mendix app you could use the Deeplink module to pass parameters. Found one topic however where it leads to an error, but if you would proceed and you have to communicate between 2 apps that would be my first thing to test if I where you.
https://forum.mendix.com/link/questions/6306
Regards