By itself it should not convince you that you’re dreaming. I don’t know if you’ve ever had a lucid dream, but often they are triggered by an oddity that you (for some reason) decide to take seriously in a particular way. A green dragon may prompt you to introspect in that way, but only if you don’t accept the mind’s trick offering. At that point it does become possible to know that you are dreaming.
By itself it should not convince you that you’re dreaming. I don’t know if you’ve ever had a lucid dream, but often they are triggered by an oddity that you (for some reason) decide to take seriously in a particular way. A green dragon may prompt you to introspect in that way, but only if you don’t accept the mind’s trick offering. At that point it does become possible to know that you are dreaming.