Yes. Searches you run from the Index tab of your dashboard are ordinary backend search requests, and they count against your usage.
They're billed, but they don't appear in your Analytics. Dashboard searches are sent with analytics: false by default, so they're excluded from your Search Analytics while still being charged.
If you're comparing your Analytics figures against your invoice and can't account for the difference, heavy dashboard use is one of the causes. See Why are the number of search requests shown in the Billing and Analytics pages different?