Yes, Content Snare works on phones. The mobile experience is fully supported and functions almost the same as the desktop version.
When a request is sent, the client receives a link. Opening that link on a phone loads a mobile-optimized version of the request where they can move through the questions one at a time. This keeps the layout simple and easy to follow, even on smaller screens:

Clients don’t have to scroll through a long form because questions appear individually, which makes the process much easier to complete. In addition, client responses are saved automatically as they type:

This means clients don’t need to manually save their progress, and they can safely leave the page and return later if needed.