I've never actually bought a GOG game before, but the sale is interesting me, but...
I actually own a few of the games listed, but they have graphical issues, like the image attached....
I'm pretty sure the answer is no, but... Would getting the GOG version change anything?

Well if you read the system requirements, you'll see that the people at GOG do try their best to get games running on modern systems and tend not to release games for sale until they do work.
You can also look at the forums for the games you are interested in to see any issues (and solutions) that the community have found. But generally, most of the games sold here do work.
I've personally only had one minor problem with one game and that was soon fixed with some basic tinkering =)

I was kinda hoping there would be a universal solution to all games with this problem, the ones I really wanted to know about where the Fallout ones, since they have this issue....
Oddly enough, I've been pestering the people at VOGONS, a forum that's dedicated to solving this kind of problems and I even went to NMA to get patches, but this is the only site that's actually told me how to use the patch in way that would fix the problem!
Thanks!

Hope it works!
As for fallout, if you already have the games, then maybe check out this thread in the fallout forum:
http://www.gog.com/en/forum/Fallout_Series/fallout_2_colors_problem
Seems like people there know more.
Otherwise, just go for it, buy them and cross your fingers ;-)

The question I now have is how do I "break" my worms game to look like that?, those are some funky colours.