Yes, you can wear non-armoured jackets while you are riding. But you should make sure that you wear a strap on armour under or over that jacket. Usually, these jackets that don’t come with armour are not meant for protection from impacts. But they can still protect you from feeling cold when you ride. The downside is that it will take you some time to wear the strap on armour. And after a while, it might become a hassle, and there is a chance that you might ditch the armour for convenience. In that case, it is better for you to get an armoured jacket.