I’m not part of the AMR team, but from my experience in programming and databases, I doubt that would be possible.
The main reason that the optimiser (and by extension, the add to bag upgrade feature, which makes use of the optimiser) is able to give you a relatively quick answer is because they do a lot of pre-processing beforehand, and have a big database of simulation data which they use AI techniques on to figure out how much of an upgrade a new item would be in your current situation. This is all done on their server infrastructure.
In order for the add to bag feature to work inside the addon, they would need to do it one of two ways.
One way would be to get everyone to download the large amount of data they use, so the calculations could be done locally on your machine, which I very much doubt would be feasible in terms of the amount of data that would need to be transferred (plus it might affect some people with low data caps), and this would need to be done each time there is change in the data. Also, it could adversely affect people’s gameplay if their computer is barely good enough to play wow, and doesn’t have extra overhead to run the algorithms required to compute the results for the add to bag feature.
The other way is the addon would need to somehow be able to communicate with their server on a regular basis via an API or something similar (essentially each time you encounter a new piece of loot). Firstly, I don’t know enough about LUA (the language WoW addons use), but I doubt Blizzard allows that kind of communication, I think it needs to be local to the computer. If this kind of communication was possible, I think AMR would have already implemented it into the rest of their features, to cut down on the copy and paste you need to do to get your gear to the website, and vice versa. Also, it wouldn’t only be yourself communicating with their server, it would be everyone using the addon, which might overwhelm their servers.
That being said, it would be a nice feature to have, but I think it would be a lot more complicated than you think to implement.
One of the AMR team can probably provide more detail on whether this would be feasible or not.