He contacted CAE to confirm that he would be eligible for the easyJet program - they checked and said it would be fine (his class 2 permits him to solo). At the end of the course you start as an FO with easyJet, so employment wise it wasn’t too much of a concern. Also the MPL is a multi-crew restricted license, so the OML would sort of exist anyways.
I think, for peace of mind, you would be best contacting CAE in a similar way just to confirm that the OML won’t be an issue. Again, all of this is specifically for the easyJet MPL - it could very well work differently at other airlines.
Hope that helps.