It will work, for testing purposes, but it really should be grounded if it's going into service for two reasons, safety, and as a starting aid for the tubes.. Computer cords for the most part are all three prong, and in the thrift stores they are like a dime a dozen just cut the end that plugs in the computer in and wire it up safely and ground it..
I know that, I just didn't want to have to go out again.