mesh with an older circuit
No, you should not do this. Grounding wires must be kept separate from conducting wires in all cases. 

First, check if the circuit you are trying to extend is truly ungrounded. Does it use metal-clad cable and metal electrical boxes like this?



If it does, the metal jacket may provide grounding for the circuit. You can try using a multimeter to measure AC voltage between the hot wire and the metal jacket. If you get about 120 volts, this is good evidence (but by no means conclusive proof) that you have a grounding system in place. You can then use two-wire-with-ground cable (e.g. 14/2 NM cable (or "romex")) to extend the circuit by bonding the bare ground conductor to the metal junction box with a green grounding screw. 



If you don't have a ground at all, then the only safe way to extend this circuit is to add a GFCI receptacle and connect the extension to the "load" terminals of the GFCI. 

This will allow you to install three-prong outlets or grounded fixtures safely on the extended circuit. These devices must not have a ground wire connected, and must be marked with a sticker that says "NO EQUIPMENT GROUND." The upstream GFCI will protect those devices in the case of a dangerous condition. Here's a diagram: