Would turning off my Apple wireless mouse make a big difference in its battery life?

Depends what sort of downtime we’re talking about, but most likely would make a difference – of course, more so if you’re not using it every waking hour, but even if you only switch it off when you go to bed, that’s still a few hours every day.

My experience has been that using Alkaline disposables seems to last a lot longer than the Li Ion rechargeables. It may have to do with sleep mode for the mouse and Bluetooth, whereby it may be pulling a very low current from the power supply even in this “sleep mode”.

I find that with one Alkaline AA I can eek out 2–3 months of use, and I even leave it switched on on my desktop unless I pack it away to travel.

I have two sets of rechargeable then just swap back and forth. Maybe every 2 months.. same with the keyboard.