Yep, it will. You're only turning the Fob on or off with that switch on the fob, just saves the battery. (in the fob) I've always turned mine off when I finish riding for the day & take it inside, just what I've always done & no issues so far. I did buy a spare new fob battery to keep on the bike in case it goes flat on me while I'm out. Yeah I know I can start using the fender method but having a new battery is also easy.
I bought the bike used. I guess it was shipped with the FOB still turned on. I never turn it off and the battery still lasts a very long time. Not sure of the purpose, really. None of my cars have on/off switches. The bike did come with a manual, but I've always been of the "reading the manual is the last resort" school of thought- but, then again, look where that got me...