that depends entirely on how you configure the checkout process.
the default eCart checkout process has no visibility to logged in / registered or not.
If you followed the "Applying Register/Login to your checkout" and "Automatically populating checkout fields" tutorials on the eCart support page, this will only set the users email address in the checkout form, if you leave the email address field as editable, then they can change the email address used for the order. the order will still be associated to the users ID. and the email address in the users table will not change (unless you add code to change it).
