Can a third-party flash made for Canon be used on a Contax G1?

You can attach third party Canon flash to a Contax camera but, because the contacts are not the same, it would be advisable to cover up or blank off all but the center contact, and then use the flash in manual mode only.

Theoretically, yes. The Canon hotshoe and the Contax G1 hotshoe are both ISO-compatible, so physically the flash should fit, and the ground (rails) and sync signal (large contact/pin in the center of the square) should be interchangeable.

However. You do want to try and do some research to find out what the safe sync voltage threshhold is for the Contax G1. Since it's a film camera, it should probably be ok, especially if you have a low-voltage digital-era Canon EX speedlite. But if you're using a vintage film-era Canon flash and the sync voltage on it is very high you may want to get a Wein Safe Sync or other voltage limiter just to be on the safe side so that you don't fry the G1's hotshoe.

Be aware, too, that you won't have anything other than sync. No TTL, no HSS, and no way to set the flash's power output other than to put it into M mode and dial in the power level you want.