Baggins: Can someone convince EA to sell to more than just on Origin?.
You'd need to give them a good reason why.
From their point of view, they get 100% of the sale price (okay, minus taxes and other sundries) when it sells through Origin. Every additional avenue they open for sales risks more people using that avenue instead of Origin. Potentially, if enough people use something other than Origin, they could possibly end up selling more copies for less overall profit.
So for any new sales channel they open, you'd have to convince them the overall gain in new customers would far outweigh existing Origin customers switching to that channel. If that channel is DRM-Free, you're likely looking at a mass exodus of Origin customers (I mean, given the choice who would choose to buy the DRM version?), and probably an overall drop in profit.
To understand the math, look at it this way (I'm intentionally using oversimplified silly numbers here. Add lots of extra zeroes to look more realistic :) )
100% of 200 customers is 200. That's Origin.
Now lets say they add GoG. This gains them 75 customers, but 100 of their Origin customers also choose to switch to GoG.
100% of 100 customers, plus 50% of 150 customers is 175. More customers, but less of the income because you're sharing the 150 customers.
For it to make sense to use GoG, there needs to be an overall raise in predicted profits for EA, taking into account all the knock-on effects of such a move. That's assuming they're even on board with the DRM-free idea in the first place, chances are someone in EA management is likely arguing that the above scenario results in 50 Origin customers, 10 GoG customers, and 2000 pirated copies.
tl;dr: It's unlikely, IMO.