No. Yes. Maybe.
All of the above are correct answers depending on the type of fare you booked.
Most cruise lines no longer will lower most fares after final payment but may offer an OBC (Onboard Credit), upgrade or other amenity. There are some fares that you can receive a lower fare and some fares you are just out of luck.
Here's the kicker. It doesn't make one bit of difference if you booked with the cruise line or a travel agent.
The "cruise myth" that you can receive some special "double secret" fare by booking with the cruise line is starting to get a bit old. Any fare you can book from the cruise line you can book through a travel agent.
I read many postings on this site from people who say that their PVP or cruise line rep was able to get them some type of fare that an agent could not. They are wrong and if the cruise line agent is telling them this then that agent should be fired or reprimanded.
So book with who you want. They all have access to the same pricing and fares.