Can I invite an injured worker if I don't know their surgery date yet?

Yes. If you don't know the surgery date, click the radio button for "No Date Set" while filling out the Invite a Patient form in the dashboard.

If the surgery date has been set by the time the patient completes their registration, they will be able to update that during their registration process. The surgery date can also be entered in the patient profile view by clicking the pencil button (located below the surgery date in the dark grey side column).