I've done it with my Graco buggy before if that helps, stripped it to the frame and put the lot in on 40C wash & it came out fine. Just if you do mean to strip the lot, put the screws back where they came from while it's washing so they don't go AWOL!
you can wash it all in the bath and leave to drip dry.
if its the newer one, you need to take the metal rod from the back of the seat, and you could possibly squeeze the seat in the machine, but it could catch and ruin the seat. hood will nee4d to be handwashed.