Shoppers see "Please sign in to get notified" on my out-of-stock products. Can guests sign up too?

Yes. That message appears because guest sign-ups are turned off. Open Plugins → In-Stock Notifier → Settings and tick Allow guest subscribers, then click Save settings. Shoppers without an account can then leave their email.

While you're there:

• Tick Email-only (hide name field) to make the form quicker.
• Check that Show the notify-me form on out-of-stock products is ticked.
• Turn on Confirmation email (on subscribe) if you want shoppers to get an email straight away.