Most of the time No, dad said it worked better dry. Once I did the letters, (and they do get white) I rinsed the tire and wheel, then used the rinsed brush to do the rest of the tire. I have a seperate rag set up to do the wheels.
They always said to start from the top and work you way down when you wash, BUT I do the tires and wheels first then finish the rest of the truck.
I also don't wipe dry the wheels and tires.....yea I know, I use a blower/vac craftsman I do believe.
I hate it when you drive down the road and see all the slopper coming off the mirrors, windows etc. So crap I blow the whole thing...