The element with 12 protons is Magnesium (Mg).
Its energy shell electronic configuration is (2,8,2)
Its valency is 2. So, it tends to lose 2 electrons instead of gaining more electrons. So, it is virtually not possible in our lives, under normal circumstances.
So, there cannot be 12 protons and 13 electrons in a single atom.
However, everything is possible in Nuclear Chemistry. Unfortunately, I'm not too well versed with it. But you may get a "Yes" answer only from a Nuclear Chemist.