Just shorting out the sensor output wire will not usually hurt the sensor. This simply grounds the output voltage to zero. Once the wiring is repaired, the circuit operates normally. Almost always, the answer is no. As noted by other posters, a cheap voltmeter will not be accurate, but will cause no damage.
Resistance measurements send voltage into a circuit and check the amount returning.
That having been said, the Egulphymobile, a car of less than four years, has gone through at least four O2 sensors, and had to have the catalytic converter replaced as well. I am disappointed in this so-called North American craftsmanship. First of all, let me state that the Paperless One does continue to feed premium gas to the Egulphymobile, even when it costs upwards of 80 cents a litre, so don't start telling me that it's the fuel. Anyway, the Paperless One would love to hear from you if you have any car horror stories similar to mine, or if you are working on the formation of an Ontario chapter of the Chrysler Lemon Owners Group. It appears that I may need to join, as I'm not accustomed to having so many things go wrong with a vehicle.