looking to ground the device to reduce RFI.
If the RFI is coming from the power supply, that may or may not work.
Safety grounds, like what the household ground system is designed for, will often just provide a path to ground for stray voltages and faults. It's not the best choice for RFI grounding, although it can do that.
It's entirely possible that the power supply, while having a grounding conductor, has zero shielding.
For RFI reduction, you want shielding and noise suppression components.
First, be sure you know where the RFI is coming from. Are you 100% sure it's coming from the power supply? Is it radiated from the power supply "through the air", or is it radiated through the power lines?
If you have a grounded power supply that meets the requirements of the device, then it won't hurt to try it, but simply adding a ground will not necessarily fix it.