"De klok heeft geen batterijen nodig."
Translation:The clock does not need batteries.
No, they're not interchangeable, but your assumption is not correct either. It has nothing to do with singular vs. plural.
"Geen" is used to negate indefinite objects. It includes the indefinite article "een" and it is often translated as "not a" or "no", but it also negates plural or uncountable indefinite objects that do not get an article.
On the other hand, "niet" negates the whole sentence, or an adjective or adverb.
See here for more details an examples: https://www.duolingo.com/comment/3734833
Nope, that wouldn't make a difference. However, if you handed me two batteries for my clock, even though it is plugged in and I don't need them, I could say: "De klok heeft de batterijen niet nodig". In that case the object is definite, so it uses "niet" instead of "geen".