Arguably it could be nullified if the payment isn't legal due to being for zero value. Under UCC §3-104, a check is only a negotiable instrument if it's an unconditional order.
UCC §3-103 defines an order as "a written instruction to pay money signed by the person giving the instruction."
So, to answer the original question - I don't think a zero-amount check is legally a check because it's not a written instruction to pay any money.
> Writing a check for $0 is not an instruction to pay.
By describing it as a check you've already acknowledged it as an instruction to pay.
> Paying $0 is equivalent to not paying.
It's equivalent in terms of the final balance, but it's not the same thing in other respects. If I sent you a check for $0, you would wonder how I got your address. There are a variety of ways that it would be different from me not sending you a check for any amount of money at all.
UCC §3-103 defines an order as "a written instruction to pay money signed by the person giving the instruction."
So, to answer the original question - I don't think a zero-amount check is legally a check because it's not a written instruction to pay any money.
http://www.ckfraud.org/UCC_provisions.html