What does this mean for the stability of the game? Will it be a noticeable improvement?
It should. Modern processors/Win10 x64 handles 64bit executions much better than 32bit ones. Along with the higher memory availability to the game, it should definitely lead to more stable FPS, less crashes and better memory management. In theory, it should help greatly, but we will have to see the final result. Hence the BETA, to check how most systems handle the game, and how the 64bit client handles most systems. I remember back when first x64 Windows started rolling out that there were improvements in FPS/memory latency, etc. in 64 bit applications (compared to identical 32bit) only due to the fact that the 64bit OS + 64bit Program had much better registry optimization. I remember reading an article about it. How windows registry in 64 bit is vastly superior to 32 bit.
One thing people tend to forget is that even low range CPUs and GPUs are enough to play today's AAA games in fluid 60 FPS. In theory, a 1GHz core/memory clock in GPU and i5/Ryzen 5 level CPU has enough raw power to compute everything. The reason why people get bad performance comes from the communication between the hardware and software which is mediated by the API. Vulkan or DirectX. (efficiency of DX and Vulkan is still low, will need to wait for prodigy kids to optimize it)
With all that in mind, optimizations to the code by updating it to 64bit should lead to improved performance.