I think it’s more about processor or maybe even hard drive operations.
DDA uses about 700 mb of RAM. At least windows’ process manager shows that much after playing for a while. 4 gb ram would probably allow some more extensive caching, but I can’t think of a good example where this would matter.
If you have other reasons to get that extra RAM, then do it, because more RAM is always more convenient and makes running multiple applications much less annoying. £20 is like, 2 small pizzas worth of money.
It probably won’t affect performance in DDA, though.