no you dont have to.
wireless mice enter standby after not using them for a certain period of time typically.
on my desktop when i had a wireless mouse i never turned it off. while true that battery life might be improved slightly by turning it off (since a standby mouse draws a very very small bit of power in that mode) its not really required.
That's what I thought. When I move the mouse again, there is a 1 second lag until the mouse works again. I bet this is the 'standby' you're talking about.