Will upgrading to 16GB of RAM improve gaming performance on integrated graphics?

Probably not. Integrated graphics are bottlenecked by the GPU itself, not RAM capacity. If you’re on single-channel 8GB, switching to dual-channel 16GB might help 10-15% due to memory bandwidth, but if you already have dual-channel 8GB, more RAM won’t speed up games. Your money is better spent on a dedicated GPU, even a cheap used one.