The answer is NO.
In the early 90s, yes, AMD or some computers manufacturer like Compaq do provide driver updates for your CPU, however it is an optional driver update to improve your CPU stability. That is an old story, because basically if you are using Windows XP and above (Windows Vista/7/8/8.1/10), Windows will automatically recognized and install the CPU drivers on your system.
To put it simple, here is the list what drivers you need to install for your computer:
Hardware that you don't have to install any driver:
1. USB 2.0
5. CPU (Central Processing Unit) or Processor
6. PSU (Power Supply Unit)
7. Battery (Laptop)
Hardware you need to install driver:
4. Wireless (inbuilt or dongle/USB wireless)
5. Bluetooth (inbuilt or dongle/USB wireless)
6. Card reader (Inbuilt only - mostly for laptop)
8. Quick launch (Mostly for HP/Compaq notebook)
9. LAN or Ethernet
10. USB 3.0
11. Webcam (Camera - inbuilt or USB)
12. Fingerprint (If your computer have one)
There are others additional drivers essential for computer with Intel Chipset such as:
MEI (Intel Management Interface)
Intel turbo Boost
Intel rapid Storage technology (Mostly for Windows 7 for fast boot)
Intel Matirx Storage Technology (Mostly for Windows XP)
Take note that you if you are using Windows Vista and above, some of the drivers automatically installed. Windows 7 normally will install all drivers except Card Reader and certain graphic driver. It is the best to check what drivers you are missing, then just download it from your computer manufacturer website.