If I modify the address of my contact, will that reflect in the invoices created for this contact?

When you modify the address of your contact - be it shipping address, billing address or both, you can make it reflect in all transactions associated with that contact. Take a look at the screenshot below to see how its done.

Note: Only the current sales orders, purchase orders, invoices in ‘Draft’ status and ‘Open’ bills will reflect the address change. Those that have progressed beyond the above mentioned statuses will not be changed.