No. The user does NOT need a copy of the invoice invitation. However, the user must be designated as an 'Invoice Contact' on the commitment associated with the invoice. See Add Invoice Contacts to a Commitment. The user must also be granted the appropriate access permissions detailed in Submit an Invoice as a Subcontractor.
How does Procore send invoice invitations?
When a Procore user creates a new billing period, that user has option to send out an automated billing invite to anyone who is either (1) named on the 'Private' list for the invoice or (2) a member of the Commitment tool's default 'Invoice Contact' list. See Start a New Billing Period and Send Invoice Emails and Create Invoice Contacts.
What do I do when an invoice contact reports an invoice invitation is lost or missing?
If an invoice contact reports that an invoice invitation or reminder email is lost or missing, let that person know they can log in to Procore and submit the invoice the Commitments tool. For instruction, see Submit an Invoice as a Subcontractor.