No, you won't be charged anything if you request an influencer's data from a private account. Because the account is private, HypeAuditor is unable to retrieve its data, so no report is generated and no credit is deducted.
You are only charged in cases where data is successfully retrieved — for example, when requesting a new report for an account not yet in your database, or when updating an expired report.
For related billing scenarios, see: - If something goes wrong during an API call, will I still be charged? - If I accidentally request the same influencer's data twice, will I be charged twice?