Yes, they can all sync to the same iTunes library. The key is the AppleID that you will be using. Are you planning on using the same AppleID and iCloud account for all users? If so, then you will want to be sure to set up the Restrictions on each iPad to require a Password for purchases immediately, so you can prevent the students from purchasing other apps on the credit card you are using for the iTunes account....
Hope this helps!
Yes. It's possible. After you read the information in the link that Ana posted, you might want to look at this.
Read the links at the bottom of the article as well.