Should I upgrade to 16GB of RAM even if my CPU is old?

Yes. RAM is cheap, and the CPU bottleneck you’re worried about is probably not as bad as you think. Your older CPU will still work fine for most tasks, and the real bottleneck is usually too little RAM. Jumping to 16GB lets you keep more tabs open and run background apps without swapping to disk, while running out of RAM makes the whole machine crawl. Only hold off if you’re on something really ancient like a Core 2 Duo and the upgrade costs more than the computer is worth.