Rules (and card) as written, there does not appear to be anything that would prevent Reinforce from being used.
However, Reinforce received errata so that it requires a Master monster to be on the map and it appears that the overlord is not able to place Master zombies.
Reinforce: The card should read, “Play this card at the end of your turn and choose a master monster on the map. Place minion monsters of that monster’s group in empty spaces adjacent to that monster, up to the group limit. These monsters may not be placed within 3 spaces of any hero, but may otherwise be placed in any empty space.”