Absolutely – In fact, using a grounded patch panel is required by the NEC
Grounding the frame of your patch panel is considered industry best practice, but the correct term would be “bonding,” which means that the metal is bonded (in direct contact) with the grounding conductor (the green or bare copper wire). The National Electric Code Handbook states that the metal patch panel should be bonded in article 250.134
Grounding is actually really important in electronics because it creates a reference ground between all of the electrical components and POE cabling is no exception.
Now Here Comes the “But” Part.
So the POE shielding (the outside layer) should be grounded, but the internal conductors of the POE cable system ground should be left floating (which means not grounded between the ends). The reasoning for this is quite complicated, but as an installer, all you need to know is that the POE internal conductors should be left floating, and the sheet should be grounded
If you need help installing some data cable, Cellar Door can help.