I'm guessing people will be able to check out late in the vast majority of cases, especially if you have a standard room. The problem is if EVERYONE is checking out at 4 pm and the hotel is sold out, than there is no way people checking in will be able to get in their room at 3 pm, the guaranteed check in time.
Now, certainly not everyone in the Swan during the time period will be using the late check out special. Many people who are staying on the special will have flights leaving much earlier and you have to take worry about getting through rush hour traffic, through airport security, etc. I imagine there are some people who will check out earlier in the day and then head to the parks and return in the evening. Then there will be lots of people who will be checking in that won't get to the hotel until much later in the evening, or they will check in early in the morning, head to the parks before they get in their room, and return to the hotel after dinner or park closing.
If you have one of the suites on club level or some other room where that is somewhat rare, then there could be a problem. They usually do these specials during times when the hotel is pretty empty, so even that shouldn't be a problem in most cases.
We couldn't check out late last month because the hotel was sold out. We weren't promised late checkout and we didn't inquire until the last day. They did let us stay in our room until 1:45 pm at no charge. Usually the late checkout is a $30 fee when they aren't running a special.
I'm sure if you let them know at check in that the late check out is very important to you and you'll leave a day early if you can't have it, then they will accomodate you.