1200watts/ 14.4volts/.7*.6= 77amps
In the equation, .7 is for efficiency and .6 is because you're probably playing music
The car uses about 50 amperes, so 77A+50A= 127A. The alt is 160A, so you should be good. That's just an estimate though.
Keep in mind that the alt is supposed to put out power at ~1700RPMs and up, and puts out less power at idle