The carpet is Nylon. Can't hurt it by doing this. Just make sure that it's really dry, including the underlay, before putting it back. Don't hit the underlay with the pressure washer. It won't like that. The underlay will hold the water longer than the carpet. If you want to, you can seperate the two, glue the underlay back into the vehicle, wash the carpet & then re-install that when it's dry. The carpet will dry out much faster this way. Use 3M '90' aerosol glue, available at most home supply stores.
Or for a little less than $300.00 you can buy new carpets. It'll come with the new underlay. Use/specify 'ACC' (Auto Craft Carpets), 'cause they ARE the best.
While the carpet is out is the perfect time to add some sound deadener. Fat Mat, Brown Bag, Insul-Shield, whatever. There is a bunch of different Co.'s. Anything is better than nothing. It makes a big difference. I like to do 2 layers on the back wall. Get enough to do your doors, too. 70% of road noise comes through the doors.