We went to WDW in April last year, and I received the same $200 offer to open a Disney Visa card, probably in February. Possibly early March, I can't remember. I just know I took advantage of the offer in time to have my card to take with me on our April trip, and I had the 200 points on my account when we went. We did Downtown Disney on the day we arrived and I just went to some place there and got a blank card. I then had to call the 800 number to claim my points and have them put on that card so that I could have some free spending money for that trip. I had charged around 400 bucks or so as of that time, because I actually had 204 rewards points available, which I redeemed onto that gift card and used on souveniers on our trip.
And they expire in 5 years. After redeeming my points in April 2010, the points that I accumulated on the next billing cycle are set to expire at some point in 2015 (I can't remember the month right off hand). So those points will expire in whatever month in 2015, the next set of points, from the following billing cycle will expire the following month, and so on.