I'm just a developer and I think curators and researchers would be in a better position to answer your questions, but I'll take a stab at this. Hopefully, others will chime in.
Since you're asking permission to contribute data I assume you don't have your own installation of Dataverse. (If you have your own installation of Dataverse you can do whatever you want with it.) Perhaps you're thinking of contributing to one of the three* Dataverse installations that accept data from anyone (Harvard Dataverse, UNC Dataverse, and Scholars Portal). You'd want to check with each on on their policies by clicking the "Support" link at the top of the installation homepage and asking your question there. I can tell you that I recently asked a curator of the Harvard Dataverse if it's ok for me to publish some data I gathered on open source projects at Harvard. (Yes, this means that I'm trying to eat my own dog food by actually using the application I hack on all day at least occasionally.) I was told that it's fine and that it's not like I have to write an academic paper about it. I can just put the data out there. If your question is more oriented toward creating an unpublished dataset that you eventually plan to published along with an article, yes, this is certainly possible and very common when using Dataverse.
You can make all the students in your class co-authors on your dataset.
* We should probably highlight these three installations somehow on the Dataverse project website because it's not obvious which of the 26 installations anyone can use.