Does TRACON airspace override Class B airspace in terms of control authority when controlling approach or departure procedures?
Class B is a legal restriction for pilots. ATC has to give them clearance to enter it. It's there to protect the traffic around a busy airport from aircraft that are not being controlled by ATC. 

The TRACON airspace is just for controllers. Pilots aren't expected to know sector boundaries. They don't have to worry about that at all. Each controller will tell the pilot the frequency to contact the next controller whose airspace they are about to enter. Few TRACONs make their sector boundaries public and they change often.

A pilot flying under VFR does not necessarily even need to talk to controllers outside of A, B, C or D airspace, regardless of what ATC sector he might be in.

As long as you have the correct type of transponder, it is entirely legal to fly VFR through the layer of air above the class B below 18,000 feet without contacting atc. (This is class E airspace). Whatever controller whose sector you're flying through will keep any IFR traffic away from you, but they don't need to give you vectors or anything. You have to stay away from clouds. It's entirely the pilot's responsibility to see and avoid things.*

SIDs and STARs are only used by IFR traffic that is being controlled by ATC, but not necessarily by TRACON the whole time. Some STARs start hundreds of miles from the airport. When they begin the arrival they will be controlled by en-route controllers, who will tell them when they need to switch to TRACON and what frequency to use. 



* I'm leaving out flight following for simplicity.