It helps, but it does not fix everything. The escutcheon protects the cylinder from force, that is, from being gripped, snapped or pulled out. But if the cylinder is basic, it can still be opened with techniques that need no force.
A basic cylinder has no defences against bumping or picking. With or without an escutcheon, those techniques work just the same, because they go in through the keyhole.
That is why the ideal is the pair: an anti-snap, anti-bump cylinder with an escutcheon covering it. If you have to choose one first, it depends on your door. If the cylinder sticks out a lot, the escutcheon makes more difference. If it does not stick out, the cylinder.
Send us a photo of your door and we will tell you. More in escutcheon installation.