I would say so. More Vram turn around between GPU and system ram would quickly start using the HDD's pagefile virtual ram.
The old card had 512MB didn't it? Can you try lower GTA settings so Vram usage is close to what it was before, to try sort of see if problem still persists?
The OS alone can use a fair bit of ram, between 2~3GB. Doesn't leave much for applications. OS would try it's best to utilise, but yeah, more ram couldn't hurt. 2x 8GB for dual channel 16GB is recommended nowadays.