Is a GPU memory increases the performance?
It depends on the type of graphics card. If you select the entry-level card with 4GB memory, it is useless. It does not have enough GPU power to run the games at high graphics settings, i.e., 1080p. Therefore, it is recommended to go for a 2GB memory for an entry-level card.
A mid-range and a high-end graphics card are better to use the 4GB memory, and it significantly increases the performance for playing games at high resolution, i.e., 1080p, 1440p, or more.