Ahh, WordPress again...Answer is no. WordPress is widely popular for being easy to use, yet has a knack to surface incredible problems in terms of maintaining updates. We see this so often it is humorous. Our customers at times even doubt our ability and fore-site to ensure the well being of their website. Truth be told, as annoying as those little red icons are, they are not mocking you and are not mandatory. Often times, the latest versions of plugins may not be compatible with other areas of your website causing unnecessary headaches.
When do I update?
Well, are you having problems? If not, forget about those annoying little circle notices and move on with peace. Now, if your website is not under the care of a decent hosting provider or a website maintenance service - (shameless plug, but you are reading this on our website) simply proceed with care. WordPress is built upon third-party development plugins. Not a bad thing if you just keep in mind that there are some bad apples out there within the realm of third-party plugins. In short, not all plugins are going to agree with your existing site configuration.