Yes it does. There’s a reason James Bond gets his martinis shaken not stirred

i always shake, it’s called a shaken iced tea ya know? not a shaken iced water with tea.

Actually yea. My SM came in one day and we were packed and she saw me making a iced tea with tea and ice then handing it out she remade two shaken ones and had me to both. The shaken tea is colder and builds consistent coolness throughout the drink with tea then ice only get the top of the drink cold

If they want the sweetener, I’ll shake it. If not, I won’t.

For standard yes, still shake it. But you could always ask the customer, do you want it shaken if they're ordering it with no water.