Does a small race do extra damage when enlarged by the Enlarge/Reduce spell?

Me and a friend were discussing gnome barbarians, and the fact that small creatures have disadvantage on an attack when using a weapon with the heavy property. I brought up that the “Enlarge/Reduce” spell would negate this disadvantage by making the gnome size class medium temporarily.

Though, the “Enlarge/Reduce” spell also causes creatures to do 1d4 extra damage with weapons they use. If a gnome/kobold/halfling/goblin were to hold a greatsword, and have a wizard enlarge them, it appears that, not only would the disadvantage imposed by being a small race be removed, but they would also do 1d4 damage more than any normally medium character using the weapon. This makes no sense to me though, am I reading everything correctly?