Earlier quoted context omitted.
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…
Hm. Is $0 not an amount of money?
?