I do not think park attendance would rise that drastically due to free parking. Parking lot capacity most surely would rise but it might also be believed in other places (ie DTD and the resorts)
Your point of the resorts attendance is however completely valid. This is shaving off a perk of being a resort guest. Disney would definitely need to look into how this would effect resort attendance.
If I had to guess the effect would be fairly minimal. Personally the $11 per day parking has never been a make or break factor on deciding on weather I stay on property or not. Now if the dynamic switched the other way (resort guest no longer get free parking) then I might think a bit differently.
If it looked like I was arguing that free parking would increase attendance, then I'm sorry; it was not my intent. I was only arguing that it may result in more cars entering the lots. Fewer people jamming themselves into one car, being uncomfotable and unsafe for however long it takes them to get to WDW from where they are. Fewer off-site visitors taking advantage of their hotel's shuttle service. Stuff like that.
However, the more I think about it, the more it's possible...POSSIBLE, that free parking might increase revenue elsewhere. People staying off-property probably factor in the cost of parking when determining where to stay. Paying for parking is worth it, for these people, when you consider what you're saving by not staying at a WDW resort. But if, on top of that, they're saving $11/day, that might be an incentive for ONE more day in the parks (and one more potential day of meals, drinks, soveneirs, etc.), or maybe even adding a previously unplanned day at one of the water parks or Pleasure Island.
However, considering that people are saving 11 bucks a carload, NOT a bucks a head, I don't think there would be enough people opting to spend that money in the parks or extending their stay to warrant the money lost elsewhere, like people not opting to stay onsite.
In regards to your last point, while it's a similar rob-Peter-to-pay-Paul scenario, I'd suspect that the cost of parking is essentially "rolled in" to the WDW resort fees. If they wanted to start charging resort guests to pay for parking at the theme parks, they'd probably hide it in an increase of the room rate so they could still advertise "stay at a WDW resort and never pay for parking at any of the theme parks!"
And in closing, please remember, a: there's no verfication for this rumor, and b: April 1st is a week away.