Am I going to encounter grounding issues with this PCB design?
I would connect both pins directly to the ground plane. You want the electric potential at these points to be as similar as possible, which means you should connect them with the lowest impedance you can. That's the ground plane.

Remember, ground isn't magic. It's just a net like any other. The charges moving in your circuit don't even know what "ground" is. Also remember that the ground current is equal to the supply current. Think about where the currents flow in your circuit, and what those currents will do when the ground connection has inductance and resistance. Usually you want ground to be as much the same voltage everywhere as possible, which means minimizing inductance and resistance at every opportunity.