No. Particularly if the equipment in question is listed by Underwriters Laboratories or another recognized testing laboratory. The voltage and frequency applied to a power supply is exactly the same. Only the grounding reference is changed.
Though unbalanced (standard) ac power has a neutral conductor, UL standards specifically prohibit the use of a neutral as a grounding reference even though it has zero volts.
If the neutral side of a power supply were to be grounded, it would immediately cause actuation of the output breaker on the balanced power system thereby shutting the system down.
Even if the ground was lifted on the ac cord and the neutral side of the power supply was improperly grounded to the chassis, touching the chassis would result in a 5 millisecond shock at only 60 Volts before the system sensors detected excess ground leakage and shut the system down.
The electrical code requires redundant safety measures be incorporated into all balanced power systems protecting both equipment and personnel from harm.