Evernote does something like this. And it let's you search for text in the images as well. I have over 12k notes in Evernote. Many screenshots. It has excellent OCR capabilities, full-text search (via Lucene?) and syncs across devices.
Evernote has traditionally been marketed as a note-taking app but for me it is a personal database/encyclopaedia. The ease of finding anything without having to worry about structure or links (though I have a bit of both) is fantastic.
It's so bad that I am actively looking for alternatives, even though I'm dreading getting my highly-formatted data out in a usable form.
I am in the exact same position. Especially so after several senior execs left the Evernote company. I even work on a custom notes store (Django and mysql backed) to keep kopies of all my notes because I really see no real alternative with the search capabilities of Evernote. And no, OneNote is not the same (search wise)