If your child is still 2, even if they turn 3 during the trip they are free (I found out some info from guest reations.) You can bring a small copy of the BC if it makes you feel better (we always do when we travel just to be careful.) But no cast memeber will ask you for it. They might ask your child how old he is. My DD is turning 3 next week and she is very excited about this and will tell anyone who listens about it.
I have heard of many people having a ticket for young 3 year olds, but strolling the kid in and never being asked for a ticket. They save the unused days for future trips.
We took DD to WDW for a total of 4 trips before she turned 3. I am not looking forward to having to pay for her next time, but what are you going to do about it? We are going to FLA in may (she will be 3 years and 1 month at that time.) We aren't planning on going to the parks but Vero Beach. However one day at MK might happen. I think if that was the case I would buy the ticket, but not present it unless they asked. If we don't need it save it for later. But I think it would be better to avoid that situation all together and enjoy the beach.
Here another bit of info. If you buy a 9 year old a park hopper pass and there are still days on it, that child (or "adult") can later use the same ticket no mater how old they get (as long as the dates macth up.) You might need to take it to GR and have them switch it for an adult hopper, but you can still use it. At least this is what I was told in the past. WDW sometimes makes changes so before doing it double check.