The answer is a resounding absolutely not!
You can see that toolbar because you’re logged into Splash as the page’s rightful owner. Just hit “Preview” in the toolbar or go to your page in a fresh browser to see what it looks like to guests.
Who else can see the toolbar? Well, if you have invited co-planners to your event page (other admins), they’ll be able to see it, too. But only if they’re logged in to Splash.