No, but unlike the mobile apps you can just ignore it.

Or use a third party app that won’t nag you.

Thanks! Just to clarify—does the application actually auto-upgrade on its own, or is it simply a notification about a new version being available? In other words, if I click the update message, will it proceed with the installation automatically?

No, it won’t proceed unless you tell it to. 
But I would question the wisdom in ignoring the update…