This is an important difference when the program is rapidly changing the period to modulate the sound. This is worthwhile noting, since the datasheets say that the chip counts down.
Also, note that period = 0 is the same as period = 1. This is mentioned in the YM2203 datasheet. However, this does NOT apply to the Envelope period. In that case, period = 0 is half as period = 1. [https://github.com/mamedev/mame/blob/master/src/devices/sound/ay8910.cpp Source](Does this last sentence apply only to the SSG or to the PSG as well?)
The tones, the noise, and envelope are never halted. All of them are continually active whether or not they're connected to an audible output.