Yes, you need to record the automation of the wah.
You can record (actually Write) automation for any synth or effect that makes automation available.
With Amplitube, you will need to go through a few setup steps to make that possible.
Obviously,you already have the Wah inserted (as stomp A?)
Now you have to make it visible to GTP4 to control the automation of the Wah.
Click the AUTOMATION button.
You will see the screen below (sort of):
In the screen shot, I have already stepped through the menu on the left, clicked ADD, and assigned the Wah to Param 1. Param 1 is what GTP will see. We'll get to that in a minute.
In your Track view, right click on the audio track where you have Amplitube inserted as an effect. Follow the Envelope path to Amplitube:
Click amplitube, and check Param 1.
This key step is where you dictate how Amplitube communicates automation with GTP4.
Now you can write automation to GTP from the Wah pedal.
Arm Automation Write (W in the track view) and hit Play(or the spacebar). Move the pedal with your mouse. As the Now Time marker progresses, your movement will be recorded and it will look something like this:
The whole thing looks more complicated than it really is, and it takes just a few seconds to set up.
Hope that helps.