So, depends on the question. Are you asking if it would be useful academically?
I got a Kindle DX as a firstie. I actually wanted it for help in reducing my book load! I had mixed results. For my English 400 course and scholar's capstone course, I loved it. Most of the books were in kindle format. I was able to takes notes and highlight passages then bring them up very easily. Another use I wanted was for my chemistry work. In my upper level chem we used and read extensively from primary research which came mostly in the form of journal articles in PDF format. Instead of printing a gazillion pages of journal articles, I could put them on the kindle. Downside: no PDF highlighting on the kindle, so it wasn't as useful.
On the up side, I loved it for traveling, especially for long trips (like my month in Europe last summer!). Instead of lugging books, my kindle saved some packing space.
As far as utility....I'd say you wouldn't be much better off honestly. If you want one because you like it and find it more convenient, go for it.
EDIT: They are not prohibited. The iPad might get some scrutiny, but the kindle/nook would not be a problem at all. 4 digs are allowed to have their own computers, so the iPad would be fine as well. Get caught listening to music or watching TV at your own risk.