With Exportify, you can definitely do exports for orders created on the current day by manually running Exportify with the end date set to tomorrow. This will export everything from your start date up to midnight on the end date.

Please note that currently, there is no way to set up a specific time of day as a filter value. So setting up your start date to anything other than 00:00 is not possible. Exportify date ranges are for whole days only.