No, it can't. Animate dead and similar spells typically have a duration of instantaneous. This means the magic is only present at their creation (and for more powerful spells/spellcasters, an aura may linger for a time). After that, the negative energy has already infused the creature and made it undead - this is a "natural" (stretching the term quite a bit) state for an undead creature, and requires no ongoing enchantment to keep it functioning.
A lot of confusion on this issue stems from the fact that the only way mortals (read: your PCs and the vast majority of NPCs) can manipulate positive and negative energy is through magic. But a dead body infused with negative energy in other ways can become undead without any "magic". A deity capable of manipulating negative energy directly can just push the energy into the creature. A place where lots of dark things have happened can naturally attract negative energy, and people who die there may rise as undead. Some undead can "infect" living targets with negative energy carried by a natural vector, like a disease or poison (like plague zombies). None of these require any magic to create the undead.
Basically, animate dead just "starts the engine", the creatures can "run" without any more magic.