Does Minecraft log out when you shut down your laptop (Mac)?

I've been wondering this because I haven't been shutting down my mac a lot so I thought I should make this a habit, but I'm worried that Minecraft will log me out of my account.

Yes completely shutting down your computer will require you to log back into Minecraft when you turn it back on again. You shouldn't have anything to worry about if you know your account information to log back in.