No. An ESTA or a valid visa only allows you to travel to the United States. Upon arrival at the airport, all passengers are checked by the American Border Guard “Customs and Border Protection”. The officers then decide whether to grant them a stay in the country. It is possible that you will be rejected even though you hold an approved ESTA however, this is happening very rarely.
Note that it is possible to lie about certain issues during the ESTA application process. Such false information could be discovered during background checks, and although the application could be approved automatically, officials will confront an applicant at the actual check-in at a US airport. Probably such an applicant will then be rejected and forced to take the next flight back to where it came from. It is therefore only logical that an approved ESTA does not guarantee access to the USA.