Sure, they can deploy anywhere they're needed.
Often, Marine aviation assets are stationed in Okinawa and Ikwakuni. Those are the options for Marines. West Coast, East Coast, Okinawa/Ikwakuni.
Hornets are the only fleet marine aircraft not in direct support of the MEU. The do rotate in and out of the Carrier Air Wings; In both cases they will be used at the discretion of geographic area commmander.
A marine hornet squadron on a carrier is just like a navy hornet squadron on a carrier (well besides the superior aviators).