Assuming a wheelchair-bound person is dropped off, is there airport staff support to help the passenger through security etc and all the way to the plane?
The SFO webpage on accessibility mentions two interesting bits of information. First thing is, of course, that you should inform your airline of all particular needs you might have, for them to make the necessary arrangements. Secondly, according to the afore-mentioned website, airline staff is approachable in both Domestic and International terminals:
Travelers requiring wheelchair assistance are encouraged to advise their airline of their needs when making flight arrangements. Upon arriving at the airport, travelers with wheelchair or other special requests should approach an airline representative for assistance.
At Domestic Terminals 1, 2, and 3, airline staff can be approached at curbside and check-in areas. At the International Terminal, please proceed to your airline's assigned counter or dial 1-6210 from specially marked phones at all terminal entry doors.
Arrangements for assistance to and from other locations at SFO can be made with your airline.
Moreover, the same page also mentions security checks with dedicated lanes for disabled passengers, and their family/helper:
Getting Through Security
As part of the Transportation Security Administration's (TSA) Diamond Self-Select program, dedicated lanes that allow families, individuals unfamiliar with air travel and travelers with special needs to go through security at their own pace are available at all SFO security checkpoints. Please visit the TSA website to learn more about screening for travelers with disabilities and medical conditions.
In general the airport staff does not automatically assist with disabled travelers. It almost always needs to be arranged through the airline on which you are traveling.
It is advisable to contact the airline in advance to request wheel chair assistance, for all airports on the travelers itinerary. They will note this in your booking record and should have wheelchairs standing by at the jetway for all intermediate and final destinations, plus will organize assist at the originating airport.
However they will not be waiting curbside when you first arrive, you will need to go inside to the airline's counter to get the ball rolling. But once they start the assist, they will take the passenger all the way to the plane, through all intermediate steps (including stops in airline lounge if the traveler has lounge entry privileges).
The wheelchair service however is not provided usually by airline staff, rather it is done by a contracting company.