It actually freezes. I haven't done a flight on A340 with their latest SimApp Pro update but my MCDU froze 2 out of 2 times in my previous flights once the compatibility was released. Liked you mentioned, buttons on the physical MCDU were responsive and made changes to the in-sim MCDU despite being on a frozen state. The only way I could get it working again during the flight was unplugging and replugging the MCDU. However, it took no longer than some 20-30 minutes until it froze again and again.
Don't wish to be frustrated, but it appears that consumers are required to debug or fly with workarounds with literally everything that are brought to the sim nowadays. Or, maybe that's just how the software world is these days. The sim that you were able to fly finally after debugging things for 2 hours require debugging/ implying workarounds in other areas the next time you touch the sim. While it's okay to do so given the hobby itself. sometimes it does get tiring to the point where you just give up the idea of doing a flight. Haha.