Not by default. The Skip images that already have alt text setting is on for new installs, which means any image that already has alt text is left completely alone and marked Skipped. The app only fills in the images that have nothing.
If you want it to replace your existing alt text as well, uncheck that box in App settings → Manage existing alt text. Be aware that this overwrites everything, including alt text you or Shopify added manually.
If you installed the app a while ago, check the state of that box — it was added in a later release, and older stores may have it switched off.