Ok, this thread is fun.
First let's start off with basic logic:
1. The P5002 is rated at 500 x 1 @ 4ohm
2. NEVER EVER use any "PEAK" numbers - those might as well be "Hit by lightning" numbers - they just are not accurate and are impossible to base any intelligent convo off of.
Ok, with that out of the way, apparentlty we have a birth sheet stating 2000W of output. I'll tell you why that would basically break the laws of physics....First, that amp has a total of two 20 or 30A fuses on it (I can't tell from the shitty photo on the net and I'm not downloading the manual). Let's give it the benefit of the doubt and go for the 30's - now that's 60A of current.
We all know fuses don't trip like circuit breakers, so let's be even more generous and say she can draw 80A at full tilt.
So, assuming a perfect charging system (14.4 v at the amp) and a perfectly efficient amplifier, this thing COULD make 1152W of power. But amps don't work that way in the real world (and neither do charging systems) so even if we give it a more than excellent 75% efficiency rating, we are looking at around 850W of actual power.
Now, that is being generous. For all intents and purposes, an 800w amp probably won't cause any problems to a HEALTHY charging system (i.e. good grounds, alternator to battery wire, and good alternator/voltage regulator, good battery). Check up on those and make sure that they are in good working order.