Grounding two points in open circuit
This would be what's happening in your circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

The current in your circuit will be:

I=(E1+E2)/(R1+R2+Rw1+Rw2+RGnd)

Where: R1 and R2 are your internal resistors; Rw1 and Rw2 are the resistance of the wires; RGnd is the resistance between your ground points you mention.

In the case those grounds are connected (like in most electronic boards), your RGnd will be 0, so there will be a lot of current flowing trough your circuit.

Otherwise, if the grounds are not electricaly connected (like two earth electrodes), then the resistance might be infinite or very high (depending on the connection to earth, the distance, etc), in that case there would be very little current flowing, or even zero current.