now that you mention it probably wouldnt...like i said i havent seen the box for myself....but looking at it you would probly see a whole mess of wires going in...several of which cut off a varity of devices...all the alarm box does is act as switch for these things...they would have to be bypassed
you have to look at a wiring diagram of how its layed out and connect the wire with voltage to the ones going to said devices...some of which could be constant or accessory depending on what they are...if your not fairly experienced with electrical I wouldnt recommend attemping a bypass, you'll probly wind up worse off than you are now
ive never had to mess with my stock alarm since mine got fryed and for some reason has not effected the car at all...but bypassing it is definately doable
a good test for ur situation is to turn the key on and check that efi main relay in the engine fuse box is getting power( both the switched circuit and the one to activate the relay)...if its not, thats ur problem right there...if you run a new accessory line into it should fix ur problem