Yes. The hitsPerPage parameter controls how many search results (hits) are returned per page. Its maximum value is 1000. You cannot request more than 1000 hits per single page of results.
Important Related Limit:
The total number of hits/pages you can access through pagination is also bound by the paginationLimitedTo setting. By default this value is 1000 results, and it can be increased up to 20,000 via index settings. This means that even if hitsPerPage is set to 1000, you may still only be able to access a limited number of total results unless you adjust paginationLimitedTo.
Use hitsPerPage to control page size, and paginationLimitedTo to control how far pagination can go.