You get whatever drivers you checked off in the config. That might be only what you need for your machine, or you can build some extras, into the kernel or as modules (I've done make modules_install separate from updating the kernel more than once, because I needed support for a new peripheral). In order to boot the machine you only need a minimal set of drivers: CPU, video, keyboard (+ port), and hard drive. Anything else you can fix later if you need to.

My experience in moving a system with a custom kernel from an Athlon64 to a Phenom II more than a decade ago was that the CPU, video, and keyboard were either the same for both or easy to figure out (CPU might have been a bit more difficult if I'd been switching between AMD and Intel, but not much), but I ended up building pretty much every possible hard drive controller driver directly into the kernel until I figured out which one the new board was using. The new system booted without issue, but I had to futz around a bit to get ALSA and other nonessentials back on track.