First, check to see for yourself if the pump is working....you should hear it on a cold start for approximately 2 minutes. It's located on the front of the car, passenger side right near the bumper. You can see it if you take off the belly cover under your car.
Should you get it fixed - yes. Although this pump is solely for emissions/"smog" control it's never a good idea, imo, to leave something broken on a car...could lead to more problems down the road.
Do you have the code(s)? This will help. Also, you probably won't feel any significant loss in power, if any, unless your vac. hoses are all shot to crap...which is possible. Clubb5 sponsor, Liberty VW can sell you the part for much less than you are being quoted. Also, a board member named Sharky is very knowledgable on this from various posts I've read...maybe he'll chime in.
For more information on the pump and it's function, here's what Bentley says:
The secondary air system blows air in behind the exhaust valve for 100 seconds during a cold start (+ 5C to + 33C coolant temperature). This produces an oxygen rich exhaust gas, causes afterburning and reduces the heating-up phase of the catalyst.
Activation occurs from the Motronic Engine Control Module -J220- via the Secondary Air Injection (AIR) pump relay -J299- to the Secondary Air Injection (AIR) solenoid valve -N112-, change-over valve and combination valve.
Additionally, after each subsequent engine start (up to max. 96C engine temperature) the secondary air system will switch in for 10 seconds during idling and will be checked by the On Board Diagnostic (OBD). When this occurs, the Oxygen sensor control must be active.
Search the forums for "SAIP" or Air Pump or Secondary Air and you should find more information. It's a common failed part.
Good luck.