Can we charge a patient for the full planned Course of Treatment (CoT) on their first visit?

This is a matter between yourself and the patient, however the general answer is, yes you can.

The patient declaration on the reverse of the FP17 / FP17O states: "I agree to pay the statutory charges for the NHS dental services I receive, unless I have completed a valid claim for free or reduced cost NHS dental services overleaf and that I may have to pay the full amount prior to treatment".