That's really cool, those Poles are doing an awesome job with both gog.com and cdprojekt, and already proved to really care about their customer's opinions.
Of course, supporting Linux for a gaming delivery system can be a bit of a jump in the dark, but they already proved to be able to take brave choices (no DRM!).
Great, yes they should build a specific Wine for each game so the user without doing anything will have the game working almost perfectly. Might be quite a big task, test the best Wine version for each game is not a quick thing, but they could increase the price of 2$ for this. I'm sure no one will say anything.
GOG doesn't really have a client. All the games you own can be downloaded directly from the website. The downloader simply provides a more convenient way of getting your game with all the goodies. Also the last few months they have started distributing new titles and they partnered with a few kickstarter projects like Carmaggedon and Two Guys from Andromeda aswell.
No, I don't think GOG would do WINE and DosBox installers. I prefer native Linux games either. Even if there are so very little.
I don't think they have native source code, since 99,999% of their games have proprietary code, and even if so, they would largely improbable port them to linux from dos.
WINE is ok, DOSBox is ok, but the real question asked here is that they provide native Linux versions/binaries, if they are present. This is the idea.