In the context of elementary algebra, which is the relevant context for the OP's question, "term" is not usually understood as a formal piece of language, but rather as a piece of human-understandable jargon which may connote monomials embedded in a larger expression, or other "bits" in a more complex formula of whatever sort.
In elementary algebra, or when manipulating complex formulas of whatever kind, "term" is commonly used to denote "that bit right there". the monomial, the thing in between the plus-signs, the number, the proposition, whatever that /bit/ is in the bigger thing, especially in this monomial-in-the-polynomial context. And so since term is commonly used in this vague, jargon-sense, I would be happy to say that "0 is a term", /depending on the context/, OP. For example. If I write " 0 + yz + x = q", then I might briskly describe this equation as having three terms on its left hand side, or LHS. Now of course, as-written, the same could be re-written by getting rid of that leading zero. But suppose for whatever reason that I want to keep it in the discussion. I might say that "the first term is zero.", or similar. Or in the re-write (getting rid of same per the rules of algebra), I might instead say that in the equation "yz + x = q", that there is no one term equal to zero, for all values of the arguments.
If I had an equation of three definite integrals which all summed to zero, then I might describe the last integral on the left hand side of the equation as "the third term of the LHS". This is imprecise, and to be done on a jargon-basis, as the speakers and doers of the math are comfortable with same jargon.
Now, it may of course happen that in a given algebraic expression, a given term assumes, for given values of the variables, parameters etc, that some particular term evaluates to zero. But a central point of elementary algebra is that expressions may assume different values as functions of their variables.