The event date can be removed from The Raiser's Edge, but this will prompt a message to display in place of the date. The message is:  A schedule has not been set up for this event.

For the new, non classic version of the form, the date configuration can be modified slightly.

Hiding the date completely requires a design customization to be implemented on the site.

Additional information regarding the event date:

End date does not show for events
How to change the date and time on an event registration form for an event