Well here is the answer I got from tech support:
To obtain this specification you would need to submit a NSCAR (Non-Standard Customer Action Request) to your local Microchip sales office at: http://www.microchip.com/sales
In order to gain a rough approximation, consider that much of the current will come from the action of measuring. Note that the load current can be fairly large, probably in the mA range when operating, due to the fact that a capacitor has to charge quickly. Since its a small cap, it will be only a short current spike, so the avereage operating current should be quite low, but this would depend on how many conversions per second you do. I'd suggest to get a better understanding of it, put a 1 ohm in series with AVss (and AVdd) and watch the results on a fast scope when doing a conversion. With 1 ohm, you can easily see 1mA as 1mV, if you need more range, use a larger resistor, but obviously you can't go too far (say a few 100 mV) before the votlage drop will invalidate your experiment.
I was really hoping they could tell me something along the lines of: Assuming you are using 5V, and taking 1Msps spread over all Analog channels, the worst cast current into AVDD would be XmA.
Well, I will hope it's not more than 5-10mA and if it is, I guess I'll have to fix it.