No, unless your on dial up.
WoW uses a very minimal amount of data, same with HB.
Id say each one only uses a few hundred mb's a month even 24/7, and HB is most likely a hell of alot less.
You can run a single instance of wow off of mobile internet like 3g connection level and play for a month on a 5gb limit, so if your on broadband then running 10 will be no issue.