Yes, you can just create a transaction (payment.transaction) and link that to SO. you can see it happening in Odoo if you purchase something on odoo's ecommerce website.  It just associates the transaction to the SO and later same transaction can be used to pay the invoice whenever it is created.

On SO it looks something like:

Thank you for your quick reply.  I didn't understand the vernacular, I suppose.  In my current system, Invoicing something meant delivering the product to the customer.  I see that is obviously not the case in Odoo.  I'm a newby in case it's not obvious

The idea of creating invoices is to denote the reception of payments. Payments can be accepted(means invoices can be created) before or after the actual delivery of products or in down payments. See the options