Short answer: No.
Long answer: Texture resolution is the size of the texture itself, which gets resized on a polygon. If you had a 1024x1024 texture on a smaller object, it would look crisp and clean. If that object were put on a really tall building, it'd be stretched over and look blurry/muddy, assuming the developer didn't allow for repeating.
However if your video card doesn't have a lot of memory, it won't support higher resolutions (or rather, you'll have graphical glitches). But if you have 1GB or more on the card, then this is less of an issue.