In order to be a good caricature artist, do you first have to know how to draw a realistic face?

It helps to understand the basics solidly before distorting it for caricatures. 

Many artists study anatomy and then use that understanding in their own work, even if they have an extremely cartoony/unrealistic style. It may not be necessary, but it's good knowledge to have. Best of luck to you.

It doesn't need to be photorealistic down to the shading, texture, and rendering, but it's an asset to know and be able to draw basic anatomy and proportions before you do caricatures.

No.