I have not done the testing in practice.
In theory, it depends on the card. While one would expect it to just give one more capacity and therefore more colors and screen size/resolution, there is a way it could improve performance.
If the added memory actually widens the data bus (goes from 32 bits wide to 64 bits wide, e.g.) there are some fancy muxing/demuxing tricks that video cards can do with memory to gain performance.
I don't know whether any of them behave that way in practice. It makes the design more complicated, and for un-upgraded cards, the mux/demux circuitry is just sitting there (expense) doing nothing unless the upgrade is installed.