It's hit or miss...
We celebrated our first and third gotcha days at WDW. Make a button that says, "Today is My Gotcha Day." All of you should wear them.
The first time we went, the guard at the turnstile at MK asked what the button meant. He reached into his wallet and gave us a front of the line pass to any ride we chose. We selected SplMtn.
When we went to SpMtn, the CM asked what the button meant and told us that at the end of our ride, we'd ride again! My DS learned quickly that he can milk this. When we went to BTMRR, he said to the CM, "It's my Gotcha Day, can we ride twice?" The CM let us! Then at SplMtn, the standby line was over an hour long. He said to the CM, "It's my Gotcha Day, can we ride twice?" I told him that was an inappropriate question because the line was so long. He didn't fuss over it and when we came to the end, the CM told us to stay put. He told the people behind us to leave and we rode again... by ourselves! At lunch and dinner, they got a free dessert with "Happy Gotcha Day" written in chocolate on them. We had lunch at CRT and dinner at FF.
The next time we went, they only got a free cookie on the BW when we were heading back to our room.
So, you never know what will happen... will the magic be granted, or not? Who knows? Being in the parks when you're celebrating is the perfect gift for you to give your DS.
BTW, our 16th Gotcha Day is on Sunday! We still celebrate each year. It was one of our happiest days ever!