If I read it right - I think the OP is asking if squadrons deploy from their home air stations. Answer in that case is yes. When I was at Cecil Field my squadron was part of Air Wing 8 on the TR. Our jets would depart Cecil and head straight for the boat. All of us enlisted types were flown from Cecil to Norfolk on C-9s a day or two before the ship was pulling out.
Yeah, as another example, prior to TSTA, COMPTUEX and later deployment, our VAQ squadron would typically fly out a few days in advance from Whidbey to Norfolk/Chambers, and operate out of there for the initial CQ period, and then fly on for good for the underway periods. It isn't like administratively "re-assigning" the command to that base, but for the out of towners, sometimes CQ has to be run from somewhere more local. I don't really know if the Lemoore squadrons have the "legs" to one way from Lemoore out to a ship in the socal operating area, but I'm certain that in those cases, they must have somewhat of a maintenance presence at the beach in North Island for any diverts/bingos/etc. Oceana is lucky in that respect, as you can do CQ from homeplate, and then have your last view of America be flying yourself out to the boat for the cruise fly off.
That all being said, for the folks that have to "det" to more forward places for CQ, that isn't like weeks or anything like a normal det. In my experience, fleet CQ is pretty quick, normally a couple days only if everything goes smoothly, so that scenario probably is not a time to really enjoy the place you are flying from the beach at.