Can I sync the pictures I currently have in Picasa on my PC with the iPhoto app on my new iPad?
Since picasa is a google property, you could integrate all your pictures to Google Plus and use their mobile app to view the pictures.

From there, you can get photos into the camera roll. This would preserve the organization of your albums in Picasa until you get them into iOS. This would be best if you only import a few pictures or don't mind re-organizing things once the pictures are on iOS.

For a more complex collection, you will want to download all the photos to your PC and then import them into Photoshop. The Windows version of iTunes can read Adobe Photoshop Album 2.0 or later as well as Adobe Photoshop Elements 3.0 or later and sync collections of photos in a way that iOS can understand. 

Perhaps someone has a better solution, but these are the best two solutions I can come up with for getting Google and Apple to play nicely together with your photos.