Well this is what i gather from your install guide. It looks like it has a user selectable timed output on the alarm. You can use this as a turbo timer. You would wire up a relay to keep power onto the ignition wire, which would keep the car running. You still wouldnt be able to arm the alarm though. Kinda pointless. In order for you to be able to arm your alarm with your TT active, you will need to wire up at least one, maybe 2 relays. Which brings me to my next question, does your TT have any outputs from it, that turn on when the TT becomes active? (other than the normal ignition outputs) I think most TT's have one or two special output wires on them, so you can hook up relays to them...What TT do you have?

13.5 @108 MPH-2.2 60ft(stupid FWD!)
S16G @ 18 PSI/FMIC/Running on MegaSquirt II (Now with sequential
fuel injection)
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-1998 Mitsubishi Eclipse RS-T- "Toy"
-1992 Plymouth Laser Turbo AWD(SOLD)
-2000 Honda CR-V(daily)