the only problem i forsee with it is that you're essentially remote starting the car with the push button, in which case you can use a standard 1100F DEI bypass module, or the pill type 555f bypass. however that's not the problem i see, how would you keep the car running without putting the key in the "run" position?? with all of DEI systems, they have the normal brake shutdown as well as over-rev and timed shut downs, it's physically impossible to bypass all of the safety shutdowns. on and BTW, the PATS sensor needs to be VERY close to the key for it to pick anything up from it.
edit: ok, i see what you're saying with the whole "run" issues i thought of. however, you would need to use a few different relays and decent sized diodes to keep the accessory and ignition powered up after initial remote start using the push button. i dunno, to me it seems more complicated than it's worth. . .
Mazda3s Grand Touring 5spd., RacingBeat Springs, F2 CAI, Corksport Rear Motor Mount, Hotchkis Sway Bars