My understanding is that it must be sent in order to have it the option to mark it as paid to show up.
I'm fighting with the same issue, which is rather frustrating. It's very unprofessional to have to send a prompt for payment to a customer that has already paid.
Even scheduling it doesn't work.
Edit: I've now found a solution to this issue.
When creating the Invoice, under the option "Invoice Method" Select "Share Invoice Manually".
Once you have the invoice ready, select the "Create" option, this will provide you with a link, you can disregard this and just select "OK".
Now the invoice will be considered to have been "Sent" by the system and will allow the payment to be added.
Do this by selecting the Invoice and then selecting the "More" option. This will then display the "Add Payment" option.
Once you've marked it as paid, you can share the finalized(and marked as paid) invoice by either using the share option to get the URL, or by downloading and emailing the Invoice PDF.
While this isn't optimal it does work.
