I would rule this one as a No.
From DDI - Minions: A minion is destroyed when it takes any damage. If a minion is missed by an attack that deals damage on a miss, the minion doesn’t take that damage.
I take this to mean that a minion can not be bloodied in the normal sense, since it either is at full HP or it is dead. A dead opponent is not considered bloodied for rules purposes so, I would rule this one, a no.
As a followup and side note; check out this link on Dying and Bloodied. Since Dying is not dead this group has indicated, and I agree, that a dying character is still considered bloodied. There seems to be a strong distinction between Dead and Dying were bloodied is concerned.
Dungeon masters take note: Creatures with enhanced powers on bloodied character status can still get them with dying characters.