Does the Transliteration module alter the existing URLs? I want to install the Transliteration module for a site on Drupal.

If I install this module, would it also change existing URLs (if I enabled it in the Pathauto module settings), or would it change just the new urls? I don't to alter the existing URLs.
The Transliteration module doesn't update anything on its own. It's the Pathauto that controls that. Just enabling the Transliteration won't do anything.

Pathauto module has a setting for what happens when an entity is updated (/admin/config/search/path/settings). This means that when you edit existing content Pathauto may change the alias depending on your settings. 

You can set it to Do nothing. Leave the old alias intact. This way you'll be able to edit old content without the alias being automatically changed. 

If you need to use some other Update action setting you'll have to remember each time when editing an "old" node to untick the option Generate automatic URL alias and use the "old" alias manually.