Nope, your staging site, local development site, or tests site won’t be counted as a site in your license.
If you are under a single site license, it should be fine to use your license key in another another site for staging/testing/development purposes as long as the domain matches these:
Here are the Top-level domains that are considered as dev or staging:
And here are the Subdomains that are considered as dev or staging:
stagingN.* (SiteGround; N is an unsigned int)
*.wpengine.com (WP Engine)
And for localhost:
localhost:* (any port)