No, a PIC is not powerful enough to use or require a kernal.

You can thing of a kernal as "DOS" (it isn't, but is analogous), it contains things like heap allocators, file handling routines for mass storage, very 'hi level' stuff compared to a PIC that just bangs a few bits around the ports.

Some of the ‘ds’ series micros have the capability to need some of this. Microchip makes these libraries as free or cheap as possible, but you’re into C compiler land there.