Is it true that revenues and expenses are also classified as current or long-term on a classified income statement?

No, the statement is false.

There is no classified income statement. The income statement would be known as a Multi-Step Income Statement.

The statement that is classified is a Classified Balance sheet and the accounts what would be classified as current or long-term would be liabilities. Assets would be classified as Current, Non-current, PP&E, an Intangibles.