No. The part that starts the reset is 093.xxx, the pusher stem for zero action. The very first thing that resets is the hammer on the back side of the movement, which resets both the chronograph seconds recording hand, and the minute recording hand. The pusher stem for zero action moves the stem bolt for hammer (1759) off to one side, allowing the hammer to drop. Here's a video demonstrating this:
You can do this with any 321, 861, 1861, 3861. The reset of the chronograph seconds and minutes is separate from the hour recorder, so as you can see I reset those and the hour recorder had not yet reset. That only happens when you press the pusher deeper to cause the operating lever to push the hammer down on the hour recording wheel.
So if the chronograph minutes and second are not resetting, it has nothing to do with the hour hammer operating lever, because that only comes into play after those have already been reset. Of course the hour hammer operating lever should be replaced if it has a hole in it - that's one of the upgrades Omega considers mandatory. But in tis case if it was actually broken, then the reset wouldn't likely work for the hour recorder at all, but the OP states that it does work sometimes.
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