Of course they could co-exist. The question is how much time and energy you want to put into it.
If it were me, I’d probably just link the logins and then add a link to the PHP application inside of WordPress. For example, if the user logs in inside WordPress it logs them into the application, then in the sidebar it has a submenu to the application with the user already logged in. Then if they logout of one make it so they log out of both.
This should be fairly easily done with sessions and wouldn’t take too much energy.
Creating a WordPress plugin would be nice, but it may be a lot more work than its value in my opinion at least.