If the ground of the DUT is floating, connecting shouldn't make much difference (apart from parasitics). If it is not, you can power the DUT from a floating power supply (battery, lab power supply). If it is at the same potential as earth ground, you can connect the ground clip to your DUT ground. Expect to see some sparks flying if you get it wrong.
The ground clip of 99% of the oscilloscopes will and should always be grounded, learn to live with it or shell out the $$$ for a differential probe (expect to pay more than for the scope). The CH1-CH2 method is a poor man's differential probe with lousy common-mode rejection ratio (don't be surprised by 50/60Hz interference).