According to Airbus Maintenance Manual, it is NOT necessary to install Lock pin if the a/c is doing a pushback for flight. Is is only necessary to instal the pin of we are towing the a/c. Airbus say it is optional to instal the pin for a regular pushback.
Having said this, my company use the Downlock pin on pushback for the 330's, for the simply reason that its attached to the bypass pin by a connecting wire. there are Remove Before Flight streamers on both pins. Its just the belt and braces method. Whats the harm. Its little or no hassle removing the Lock pin from the 330. And as they are both attaced to each other, it is virtually impossible to forget to remove them both.
A few years back our companies Engineering Dept sent Query Notes to Airbus and Boeing asking them the question Are Downlock pins required for pushback in relation to positioning the a/c for flight. Both Replied with NO. only the steering bypass pin is required.
I heard lately that a certain airlines flight out of DXB, the captain refused to allow the a/c to be pushed back without the Nose downlock installed!! He delayed the a/c departure. Turned out he was in the wrong. company MOE stated only bypass needed and this was of course stated in the M.M. also. Suppose he was just used to seeing us display both pins on pushback as we use them both out of habit.