At best, EA could bring DA2 and ME2 on GOG. But ME3 and DAI are using the Origin infrastructure for the MP side. And while they can cut those at some point, that time is not know. Both the DA:I and ME3 MP are still alive and kicking. And i did not have troubles getting into those at any given time, which is amazing, considering how old are those games.
@mcsupersport EA actually has a rather nice number of games on GOG. So it's not quite far-fetched to assume that they are happy cooperating with GOG. Yes, mostly are old games, but i will point towards a GOG exclusive: the only place where you will find legally and working a copy of Sim City 3000 is GOG. You do not offer exclusives, if you are not happy with that cooperation. GOG can bring life back into old games (they have a really good knowhow in the matter), EA can profit from selling old games again. It's also good for consumers, as GOG goes to incredible lengths to keep those old games playable.
What is puzzling, is why EA doesn't add those versions into Origin, as a lot of those games are present there and lack the updates brought by GOG (i have a few old EA games on Origin, but i have even more on GOG and i can tell the difference in the support for modern OS). One would think that EA would chose to have the superior versions on both platforms. Probably certain terms in the contract prevents them to use the improvements made by GOG to make the games to work on the modern OS.
GOG was able to restore MP content for certain games, but in the case of ME3 and DA:I, the online parts are deeply embedded with Origin. And the only possible way to deal with it, would probably be to cut that completely (which would be a real pain).
I am mildly optimistical when it comes to ME1, ME2 and DA2, though. Those could probably be brought on GOG, without many problems.