Does the timer interval I place upon an automatic sugar cane farm actually affect the production rate in any way? The timer I am using is not a BUD switch or anything overly fancy, just a simple hopper timer. But since sugar canes grow due to random block updates, assuming that the pulse for the pistons I use to harvest the sugarcane is negligibly short compared to the timescale of harvest, shouldn't the interval set on the hopper not affect the amount of sugarcane harvested? Or does the extending piston mess with the growth of the sugar cane?
The piston-arm over the sugarcane resets the amount of time it needs to grow, so the answer is yes, it does affect the amount of sugar canes, i recommend you to put a bud switch, its very easy to do and its very efficient.
You can also put a timer with a lot of time, so you are sure that the sugar cane will be growth when its harvested.
Try my farming system: I used an Inverted Daylight Sensor to power a redstone wire (you can make the wire about 5-7 blocks long), connected to a redstone repeater, and then continue with the wire and repeaters, to power the pistons only at evening. This way, you leave them untouched almost an entire day (not night) to grow. Even if the production is low this way, it is automated.
Regarding the time reset for sugar cane age, it resets if the sugar cane was 2 or more blocks tall, because the block that increases in age is the top one, and it is harvested, resetting the age.