According to that article (and what I've heard elsewhere) pay-per-ride vehicles will have to pay the full fee (though only once per day).
I certainly believe someone on the NY government side did their homework, because they'll make a lot of money on this, but again, I just don't understand what Uber thinks it will gain. Their drivers are the traffic.
Congestion charge is a daily fee, so unlike a toll where you pay each time you use the crossing you pay a flat fee regardless of whether you spend five minutes in Manhattan dropping off or you turn up at 5am and spend the next 18 hours driving around. I guess what it will also do therefore is encourage drivers to do more rides, because obviously the more rides they do the lower the impact of the charge on their per ride take.
Not being privy to any real data I can only take your word for it, but I would suggest that without real evidence that there is a sizeable amount of personal traffic that for whatever reason you aren't seeing, this wouldn't make sense for anyone.