Hi,yes they can as long as your employer registers your partner as a dependant of yours. They are allowed to stay on for the duration of your contract, and when your GOP is cancelled they will then be required to leave the country as they have no status in the country. If you then want to come back into the country with a 3 month tourist visa you will have to leave and re-enter. Hope this answers your question.
Anna, I am married so I cannot comment, however I can say that some of my friends who live on the island have their girlfriends live with them on their GOP's. So I guess let your partner's employer try to get you on his GOP, it's worth a try.