Neither should cause any damage. Neither is a good way to actually listen to any music, but neither should damage anything.
I am not sure how much it will help you with "testing" to see if things work, as you may get a loud hum without a ground for the turntable, though it depends on all of the particulars. And the sound will be way off hooking up to a line level input, as it will be far too soft, and the frequency response will be very bad if we are talking about a typical magnetic cartridge.