If the user is a director or track director, they will always be able to submit, regardless of the deadline. Otherwise, the server's current date must be between the "submissions accepted" date and the "submissions close" date, inclusive, as defined on the conference's Timeline page, or the user will not be able to *begin* the submission. Submissions can always be completed once they've been started, even if that happens after the close date. (In that case it's up to editorial discretion.) Note that submissions will still be accepted on the submissions close date.
The code that checks to see whether new submissions should be allowed is in pages/author/SubmitHandler.inc.php, in the "validate" function; it calls e.g. SchedConfAction::submissionsOpen to check the dates.
Public Knowledge Project Team