I suspect it might be scriptable, but out of the box, no, there’s no way to do this.
Personally if I was not wanting to use the artwork right away i would leave the fonts missing rather then swap them to something that the customer may not want. That way when the job actually needs to be done you can handle each font problem at a time.
Yes, with several hundred documents, I'd probably just buy the fonts. Save you a lot of work.
If the documents are properly set up with paragraph and character styles, you'd be able to "import styles" from a document that has style definitions using the new fonts. But any local overrides will stay unless you remove overrides, which may drop some formatting that you actually want to keep (subscripts and italics that were done with keyboard shortcuts instead of character styles, for instance).
It would probably also be possible to export the documents as tagged text, then in a text editor very carefully examine the lines where the old font names show up and globally replace those codes with codes for the new font taken from a tagged text document exported from a file with the new fonts... but that could be more work than using the "find fonts" feature, and I'm sure there are ways it could go wrong.