No, the clock will reset instantly as usual, and it would basically subtract one tick total from the regrowth rate for that particular herb for that particular cycle

In practice you will never actually pick anything when the timer is zero, because as soon as it hits zero, the common event will activate and reset the timer back to whatever the tick length is.

However, if you DO pick it during that 1/500th of a second or whatever, here's what would happen:

1. Your herb would have its regrowth rate set to its normal time
2. Clock resets and regrowth is decremented by 1

And that's it, basically. All that would happen is that the herb effectively grows one tick faster for that cycle. The next time you pick it, it would behave as it normally would.