What you are doing is trading the ability to pick your cabin for the lower price.
The categories that GTY cabins are available for varies from week to week as inventory on that cruise changes. Generally, they are available for the lower categories (11,12), and sometimes 8,9, 10. If you book a GTY11, there is no chance that you will be assigned a 12. You will be assigned a minimum of an 11, but frequently an 8 or 9.
When you get your documents, you might have a room number assigned. Alternatively, you might not have a room number until you get to the port (or you can call them a week or so ahead if they/TA haven't called you). Once you are assigned a room, it can still be changed, but it won't be changed to a lower category. For instance, if you book a GTY 11 and are assigned to a 9 when you get your docs, they will not move you back down to an 11. They might move you to a different 9 or to a 7 or whatever.
Basically, this gives
DCL a way to control their inventory and allow for people who book but fail to make the final payment by 60 days, allow for large agencies that "block" large numbers of cabins which they then either sell or return to DCL inventory by a certain date, etc. DCL is essentially committing to a place for your party on the ship, but they can decide where you will be.
Even if you do not know your assigned room until you get to the port, the luggage people have a name/cabin number list. Your bags will get to your cabin correctly. Just use the tags that DCL provides to you.
There is no promise that you will be upgraded, so don't book a category lower than one that you can be happy in. I don't know about time of year to be upgraded. It rather depends on what cabins sell out. DCL is less likely to offer a GTY room when they expect the ship to fill.
Some travel agents might know about this. You can book it thru DCL directly, then transfer your reservation to a discount agent and get their discount as well.
As to how much lower the rate is. ..If you book a GTY 11, you pay the category 11 rate. IF you sail in an 11, you didn't get a price break. If you sail in a 7, you've saved several hundred dollars.
If you really care about which room you have or even which category you have, don't book this way. If you care about saving some money, this is a good way to go. We've been on almost every deck, and I've found good and bad about each. We've never had a "bad" room...we've either been lucky or there really aren't bad cabins.....
I'v a veteran of 10 Magic cruises.