Yes, it can. ANYTHING you get inside ANY electronic component, aside from air, can "mess it up". Shampoo contains liquids and solids, and is likely to flow beyond just the point where you can see. However, I don't think I'd recommend that you try to fix it yourself and you'll likely just make it worse. If you were inclined to try doing so anyway, 90% isopropyl alcohol would be the medium you'd want to use to clean it up but without the unit apart you may just thin the shampoo and cause it to reach further inside the unit. Either try it as is or take it for repair.
Since you stand to create further complications it might simply be a good idea to allow it to completely dry before you attempt to use any of those USB ports. After the...