Is a clearance needed to depart a helipad in class B airspace?
The "Wedding Cake" literally defines the airspace, so for a the sectional part you listed above, the floor of the Class-B is at 3000 feet in the outer ring and 2000 feet in the inner ring, these heights are MSL. 

Anything outside of the wedding cake is not Class B airspace. You may be confusing the Class B airspace with the Mode-C Veil that surrounds 30nm outside of most Class B airports, which only requires that you have an operating transponder, you are still allowed to fly around VFR squawking 1200 below the Class-B without any clearance.

The airspace under the wedding cake, provided you are not within a Class-E airport, is most likely Class-G. So no, you are not required to contact Tower until you want to enter Class-B airspace or if you need a departure clearance for IFR operations.