It never hurts to ask. As Cruise Fanatic said, it's going to depend on the rate code most likely. Some cruise lines are more flexible than others after the final due date. I doubt your TA would mind checking at all. That's their job as your agent.
Joarc,
You are not "bugging" your TA. Handling requests such as yours are part of the job. We'd rather hear from you and have the opportunity to help you, rather than you worry about bothering us. Handling requests after the sale is one of the biggest parts of the TA's job and one my favorite parts because that's where really good customer service shows