Sure. There is no difference in the maintenance of the new[er] iPads. As far as backing it up, moving apps around, etc - they are the same product.
Marilyn
EDIT TO ADD: Unless, of course, you are talking about updating the iOS. That, you can do wirelessly via Apple's over-the-air update available in your Settings app (under the General tab). Granted, the iPad1 can do this (the OTA ability came with iOS 5) - but since there are no iOS updates for the iPad1 any longer, you don't do updates on it.
So, to recap: you can do everything with the new iPad you could do with the older one. But - you don't have to connect it to iTunes to update the iOS as that can be done OTA.