The answer is "No, not really" -- unless you stay at a resort with a Business Center (and really, Coronado Springs is the only one that qualifies for that - and there is a charge to use it) you don't have any internet access in the resorts.
Even with a laptop, the moderates have internet access with a wired connection, there is no wireless. And many of the value resorts don't even have that. I've brought a laptop along in the past and never used it.
I agree that your best bet is to get yourself a smartphone that has internet access is you need it that badly while away from home. Personally, I have an iPhone and that is all I take along to WDW for the weeks when I go now. Before that, it was my Blackberry.
WDW isn't really set up for business visitors.