How is your hot air intake (HAI) set up? Is it long enough to directly connect to the throttle body or do you have to connect it to the intake resonator?
The throttle body has a position sensor (TPS) internal to the throttle body. On your intake tube, running from the filter housing to the intake resonator, with will have an intake air temp (IAT) sensor. Mass air flow (MAF) sensors did not get introduced until 2006.
When you say, "black little plug" are you talking about the plug on the right side of the box that says VORTEC (intake resonator)? If so, that is a vacuum line for the fuel pressure regulator. On my 07 TB that vacuum line is actually capped off.
If you bought an intake specifically for your 03 TB (That reaches to the throttle body), then you will have four ports on the intake tube. One is for the IAT sensor, second will be for the vacuum line for the fuel pressure regulator, third will be on the underside of the intake tube if your TB has air injection, and lastly will be for the crankcase vent hose.
I would lose the stock air box and also lose the intake resonator. I have mine removed and think you get a much better sound out of the engine and exhaust with the resonator removed. If your intake tube is not long enough to connect to the throttle body, that can be resolved with a piece of PVC pipe that is 8" long, 3.5" OD. You will need to pick up a couple extra couplings, hose clamps, barb fittings, and hose. You will have to drill into the PVC to add all of the necessary ports.
Much easier to go with a K&N performance intake. All of the ports, hoses, and fitting are already supplied. Plus the intake tube runs directly to the throttle body so you can delete the intake resonator while you are at it.
In regards to a PCM tune, deleting the intake resonator has no bearing on the tune. The order sheet will ask if you have a performance intake, thats it.