If you have contact "A", and he has 2 Invoices, each totaling $100.00, the plugin should add these together and display the total of both on the contact. So in this case our 'Total Invoiced Amount' would be $200.00.
If this is what you are trying to do, then yes you can use a plugin. The plugin should do something like this:
On invoice - create/update (filtering: totalamount), you want to get the Customer of the invoice. It the customer is a contact, retrieve all Invoices for the contact, and sum the total amounts (you can use fetch aggregate). Then update the contact with the new total.
You would also want to consider the possibility of someone deleting an invoice, or changing the Customer of an invoice, so you should handle these scenarios as well (for example, running the plugin on delete as well, and disabling the Customer lookup after the invoice is created).