Is it possible to change the _alt_ text wording for images in one place?
If the images are all inline (i.e. part of the body content of the node) then there is no easy way to change the alt text in one place because these images have not been abstracted into the Drupal system. If these were fields or part of the files table, it might be possible to quickly update these using PhpMyAdmin or some other database solution but at this point your best options are


brute force (just what it sounds like, a painful node-by-node fixin' of the alt text). 
try a search and replace option of the body text. I've used the scanner module for this kind of operation and recommend it as it has robust regex support and (most importantly) a rollback option.


Neither of these are great options but they're the best you can do given the circumstances. Which to choose depends on a). how many nodes you have to deal with, and what kind of alt text you have to add. If you're adding the same alt text to every image, scanner is your answer but if you have to evaluate and update each image with appropriate alt text (ex for 508 compliance), brute force is the way to go.