If your message is irrelevant, no amount of structure will save it. On the other hand, if the message is important / relevant / worthy, then structure is vital to effectively communicating it.
That doesn't mean the structure has to be complex, just that you need to consider it.
If your message is simple, eg "Dyslexics rule. KO.", the structure pretty much sets itself.
On the other hand, if you're writing an article that explains what dyslexia is, explores the reasons why it occurs, and suggests possible strategies for managing it, then it's equally obvious that you'll need a structure that has the power to attract the interest of potential readers, then the structural flow to engage and hold them through your message, to your conclusion/s.
In simple terms amy piece of written communication should have a beginning, a middle, and an end. Even that short 'Dyslexics rule' example has stopping power, interest, flow, and conclusion.
If you're interested, I've recently published a Hub about the very subject, which I won't link here (not good HubPages etiquette), but if you click to my profile page you'll have no trouble finding it.
Good question. Cheers.