Plastic case - DC psu - grounding needed?

I'm printing a little case for a ITX build that will use a PicoPSU.

As the base will be plastic there won't be a "chassis ground," and since the PicoPSU uses an external brick for AC/DC conversion I won't have an actual path to my mains ground - at least not a normal one through the tray like you'd see in a regular case.

The motherboard is the only device in this system. Would it be a good idea to try and ground one of the mounting holes on the mobo to the negative terminal on the barrel connector that the DC brick plugs into?

No, don't worry about it. A metal case doesn't provide any ground path that isn't already handled by the other components.

Cases aren't metal to provide a ground. A metal case is grounded because it's conductive. Doing so is a precaution/safety measure (and can sometimes help with RF/EMI interference). A non-conductive case, obviously, doesn't need to be grounded and no substitute path is required.

yup. all of the 12+ raspi at my work are in plastic cases, no problems.