Yes and no, it depends on what you put into the texture it self. A way you can look at it is like this, imagine you have a plane which is 100 x 100 (Just a size, not pixel) and you add a texture at a 512 x 512 (This is pixel size) resolution, it will fill those 100 x 100 size units. Now if you add a 4096 x 4096 such texture can hold more details. which will show up on the 100 x 100 as well. The reason I say yes and no, is because if you fill the 4096 x 4096 with poor quality stuff, it might look slightly better, but wont make use of what you could get from the texture if you added high quality stuff to it.

But assuming that you do, then yes a higher resolution texture will make better quality.