[noonat]

Yes. iTunes on your desktop machine can store (and update) apps that you are not currently syncing to the device. Then, when syncing the iPad, you can check a box in iTunes to indicate that the app should be included on the device.

[Someone]

I think ~Yes/No~ is the better answer. You can remove apps and sync them from a backup later, or even download them from Apple, but AFAIK the only way to restore an app and its user state ('where was I', login info, preferences, etc) is by doing a full restore of a backup (all apps installed at a given time and their stare, plus all device settings from that time)