Well, you could do it but the ITPS will be seeing a constant voltage which will drain your battery. The ITPS is designed to get a constant voltage from the battery on one pin and switched voltage from your ACC line on another pin (look at the schematic from the ITPS site). If you hard wire the ACC line on your ITPS to the constant 12V then it will work, but again it will drain your battery. The only other option is to wire a switch in line with the ACC line on your ITPS so when you hard wire it into the constant 12V on your SUV, you can switch it on and off. Just don't forget to unswitch it when the vehicle is turned off.
Oh Yeah, you can use the DC plug that came with your power supply (I'm assuming you're talking about the AC to DC converter brick) but you will have to hack it off of the AC to DC brick. Just go to Radio Shack and buy a DC plug with cable and use that. Also, put a 10amp fuse in line i you do decide to do it.
If you need a diagram of this then PM me and I'll whip one together.