As mentioned, and even though you always have the last resort to make accessibility fixes with Acrobat directly on the PDF, it's always better to set all features in the native format.
InDesign gives you the chance to add Alt text by:
- Selecting an image that does not have alt text with the Selection tool.
- Choosing the by clicking on the top menu Object > Object Export Options.
- Selecting the Alt Text tab in the Object Export Options dialog box.
- Choosing Custom from the Alt Text Source menu.
- Entering the description in the text field, and clicking Done.