If you are fully linked, then anyone in the other reservations can make changes to your plans as if they were in your reservation. So yes, it is possible for them to cancel reservations you have booked.
To prevent this, you can have your reservations linked for dining only. I have cruised where we have been fully linked and cruises where I have asked to be linked for dining only. When we requested to just be linked for dining, the res agents had difficulty doing that but I think it was because the first one fully linked us and the 2nd and 3rd didn't understand there was a difference. If it is going to be an issue to be fully linked, make sure you speak to someone who sounds like they know what they are talking about and then check your reservation (if you can see the other booking to add port excursions, adult dining, etc. then they can see yours too.)
