Stock alternators should provide enough amps to run the car and charge the battery and have around 40% of their rating leftover after that. This is a very general rule, but in the absence of more information specific to this situation, it's a good starting point.
40% extra from an 180A alt would mean about 72A is available for something like an aftermarket sound system.
Using the 1700w RMS number as a starting point, and assuming the peak wattage rating on the amp(s) is double the RMS rating, that gives us 50% to use in the next calculation for actual current draw from the amps.
Normally, the sum of all the amps' onboard fuses can be multiplied by that percentage above to arrive at a rough estimate of how many amps the alternator will have to provide to power the sound system. Since we don't any amp specifics, I'll use some fuse ratings I've seen for amps I've run in the past - 150A.
50% of 150A is 75A, which is slightly more than the 72A estimation of available power from the 180A alternator.
So given all this, assumptions and generalizations aside, we can predict that trying to power a 1700w RMS sound system with the 180A alternator will be very difficult to do without signs or symptoms of low voltage showing up somewhere on the car.
For kicks and giggles, if we plug in 220A instead of 180A to see if the upgraded Dodge alternator would fare any better, we get 88A as the reserve number from the alternator available to a sound system.
Using the 75A estimate for actual amps needed to power the system above, the 220A alternator would seem to be able to do the job for us, certainly it has a better chance of doing so than the 180A alt, all things considered.