[stvn66]

I use Dropbox's native app on android to do what you are describing. I am not sure when they starting making 2-way sync possible but I have used it for a few months now. I just tested a few different ways and every one worked.

I navigate to the file using the Dropbox app, select the file to have it download it onto my android device. When you open the file from Dropbox, it uses their native reader but you can get a different one by selecting the menu > Open with ... option. I then make annotations on my android device using the Adobe Reader App and when I close out the changes are saved.

On the computer, I use the Windows version of Foxit PDF on Linux/Windows (Adobe Pro would work also). Foxit has an Android App that works similar to Adobe's, I chose Adobe's because it had a smaller footprint at the time and now I am familiar with it's interface.

Alternatively, you can navigate to the files Dropbox downloads using your android file navigator, where your dropbox root folder is here:
~/android/data/com.dropbox.android/files/random-##s-ABCs/scratch/
make annotations, and then when you close out, they sync.

I tried both favoriting a file, and not favoriting it. Either way, the changes are synced from android to the servers and then to my computer. I would expect favoriting the file to make sure computer annotations are synced to the android. I just tested it and the favorited file on Android did not update to have the changes made on my Computer until navigating to the folder in the Dropbox App. I had already opened the file in Adobe and when I went back to in (using the recent apps button), it had updated without needing to re-open the file.