From their website they have several computing clusters
http://www.renci.org/resources/computing. One of these has Nvidia Tesla GPU's which could be suitable for mining. The question is could someone be mining on their clusters and would they have have enough hash rate to have any effect on the network?
Yes, they could use the Tesla's for mining and someone probably did. After exchanging their bitcoins for cash they realized they would never pay off the expenses of running the supercomputer to mine and gave up.