You can change the form action to admin-ajax.php?action=your_action and this will work, but it’s not best practice.
The ajax submition should be added via javascript, not by changing the form action (also your js function should prevent the form from submiting normally, returning false – see here an example: http://net.tutsplus.com/tutorials/javascript-ajax/submit-a-form-without-page-refresh-using-jquery/), and php handling of the data (on the page the form action is poing to) should be present as fallback.