Is using modals more #efficient than calling a new page to make updates to database tables?

Yes, it is. It provides better user experience. We can see that from comparing the two ways of making updates:

1. Normally we make updates to database tables by 1) submitting an HTML form from the current page to the file (specified by the form action attribute) on the server, 2) then the browser will send the form data to that file on the server which will do the updates to database tables, 3) next it will be redirected to another file (which is different from the file that the form data being sent to) and display it by refreshing the current page.
2. By using the load jQuery method (AJAX) we load a new page from the server and place it into the modal-body element, which doesn’t require the browser loading a whole new page but only updating part of the current page (which is the modal-body element).