Can the air compressor (in the back) inflate your tires?

[HummerJim]

YES, that's what it is for to reinflate your tires after you air down offroad. If you go down to around 8 psi, to bring them back up to 37 psi takes about 5 minutes each tire (been there done that many times), so give yourself lots of time.
I carry two bottles of Hutchison's fast air bomb and seal under the back seat for when I want to do more than one tire at the same time and get out of Dodge! One bottle will do a stock H2 tire from 8 to 37psi in about 40 seconds.