We are using PHP strtotime()function to parse date format, so it should basically parse about any English textual datetime description. I would recommend using the MySQL DATETIME format (YYYY-MM-DD hh:mm:ss), i.e.:
P.S. Just to be sure – our start_date, end_date and not_date_limit shortcode attributes will set the effective date(s) for the shortcode, but not the “Date range” to check product sales in (i.e. this will still be taken from what you’ve set in “Date range” option in “WooCommerce > Settings > Maximum Products per User > General”).
Hope that helps. Please let me know if you have any questions.