it depends. There is plenty of anecdotal evidence that a 60A alt can sufficiently power a 1000w rms system, but others have had trouble with a lot less.
Personally - I had a car with a 75A alt. A lot of enthusiast owners of that particular car believed the alt was undersized W/O any aftermarket electronics. Regardless, I went ahead and installed a 1000w+ system. It wasn't ideal, but it ran ok for 2 yrs or so.
Efficiency of your amplifiers plays a huge role in what your alternator will support wattage wise. You might have 2 different amps that produce 1,000 watts RMS but one only uses 50 amps for example versus 100 amps.