I was wondering if it would be alright if I tapped both the 12v Continuous & 12v ignition to a 12v Ignition source...

This way my defi's ONLY turn on when my car is started...

The downside is that everytime I shut off the car, my PEAK boost and boost warning set will reset back to default..
The reason I did this is because I dont want the Defi's to turn on when im just listening to music with car off...

Will this affect/damage the control unit since it has NO 12v continuous and gets switched in either ON or OFF state??

btw this is for my bmw 335i...

If you tap a continuous circuit they won't shut off.

theres a way to wire it so that it doesnt turn on when ur listenting to the radio and only when the key is in the on position

^^ Exactly. Wire the continuous 12V like you are supposed to so you won't loose your settings. Then wire the 12V ignition wire to a source that is only hot with the key in the ON position. That way, when the key is in the ACC position (listening to the radio), the gauges are off.

I wired my Defis this way so I wouldn't have to listen to the oil pressure warning buzzer when just listening to the radio.