As mentioned, you definitely can try to apply a new discount to an already existing booking. However, by definition, room only is just that, a booking for a room with no tickets or dining. So if you have a package, but they offer a room only discount, you would need to switch to the room only booking, buy your tickets separately, and not be eligible for the dining package. But in this scenario you are free to buy your tickets through a 3rd party like Undercover Tourist, and potentially save $5-40 on each ticket over what WDW would have charged you. The only time you need to buy tickets from WDW is if you are indeed doing a package and want dining.
The same applies for free dining. If you booked a room only reservation, and they then announce free dining, you would need to convert the room only booking to a package that meets the minimum for the free dining promotion, which is usually room, tickets, and dining. Lately I believe they were requiring you to buy a 2 or 3 day ticket minimum. This is mostly a problem if you already had existing non expiring tickets, APs, etc.
Keep in mind that WDW will usually only tell you the price for exactly what you ask. If you ask "Can I apply this discount to my booking" they may or may not tell you that a similar room at ASSp is eligible under the discount if you are currently booked at ASMu and there are no rooms available there under the discount. You can then proceed to ask if there are any comparable rooms that are eligible, but they normally won't just volunteer this information up. That is a benefit to booking with one of the TAs that specialize in Disney as they usually do a better job of trying to hit your budget with any and all available options.