No, not unless you SEVERELY over load it, which I doubt you could. While I know of one case where one blew up on somebody, that was from putting several thousands of volts into one that shouldn't have had more than about 300 impressed on it. I was a diesel mechanic in a previous work life and did quite well on the electrical side of things, especially on exams. What you'd be doing is checking the potential between the pc case and some ground, which isn't really any different than if you put across a battery (DC) or across your household electrical outlet. The meter won't conduct current unless you've got it set to measure current, so don't do that if it's a multi-meter. Otherwise, as I said, you're just measuring potential. If you get 50V, that's how much is leaking across that wire. NOTE 30VAC is enough to kill you, so I suggest you don't screw around with this issue. If you've got leakage to ground from a power supply or something on that pc case you are playing with danger. Usually these things don't get better - they get worse.
EDIT
Do I have to point out that you don't hold the metal prongs of the meter leads in your hands?? It should go without saying that you need to be insulated, but assumptions can be dangerous.