No, the $25 ($19 for kids) does not get you admission to the beach. You can walk around the property- they give you a wrist band to wear - but access to the beach and pools is not permitted. Buy your Dig tickets in the center of the Casino - You will see a big blue-green globe over the kiosk. I wish that I had asked for a map of the property. We had to keep asking directions.
We took a taxi over to Atlantis and back - dropped you right off at the front door - no 15 minute walk from the water taxi terminal as on the Disney Excursion. You don't get a guided tour either when you do it on your own, unless you happen to "tag along" with a tour group. The taxi costs $ 4 pp each way + tip.
It was a few dollars more to "do it on our own".
Atlantis was over-rated. Yes, the resort was beautiful, the fish tanks and the dig were nice - but not as great as described. I had more fun at the Baltimore Aquarium - they at least had a dolphin show ( and for a lot less $$$ ). Even SeaWorld was better.
I think that both excursions include the cost of the water taxi - you could "do" the beach day and purchase your own admission to the Dig. Also, the water taxi is $ 6 pp round trip if you want to do that on your own.