Can we run dbcc checkdb on tempdb?
The short answer to this question is “yes but do you really need to do this?”.
Actually checkdb on tempdb does not run properly as you can not have a snapshot of tempdb. Realistically you do not have to bother a lot for a possible corruption of tempdb as it is purely temporarily and it gets recreated from scratch each time you restart the server.
For more details, please refer to http://blog.consultdba.com/2010/05/dbcc-checkdb-and-tempdb.html
I will run a test by myself sometime later and have another post on this with observations.