Can you fit a text game with pictures in a 64kb download? Kind of like this screenshot. It's for a game jam...

Depends on the tools you're using. If you're making a game for an 8bit computer then the ROM you create could definitely be under 64kb

Would unity work?

I did not understand if you are using the Unity tool, but a game of the kind I saw in your screen-shot, in my opinion, can be developed with less heavier but slightly more demanding systems; such as Visual Basic, Delphi, or Visual C. This will you to reduce memory occupation. If you then compress the texts with the Lempel-Ziv algorithm (Zip archives), and keep them in compressed memory, decompressing them only when you view them, this allow you to further reduce the space required. For the images you could encode them as 4-color BMP-Windows (this format still exists), compressing it with the Run-Length algorithm (RLE, supported by BMP-Windows format). I think that doing so it you should succeed!

No, Unity wouldnt work.