Yes, they will. Microcode is hot-loaded. There is no way to permanently update a CPU's microcode; it is uploaded to the CPU on each OS boot. They come packaged in the appropriate Windows update or macOS update, or for example on Ubuntu you'll get them the next time you upgrade with apt. So to answer your question, the next time the user updates their operating system, provided the OS manufacturer has included the new firmware, the user will automatically get the new microcode which will get patched onto the CPU on each boot of that OS from then onwards.