Is there danger to running a computer without it being in a case? I'm under the impression that the motherboard mounts also act as grounding points for the board
Not really a danger as long as the mobo is on a surface that doesn't conduct/transfer static electricity and kids/dust/pets/liquids are kept away. Typically having the mobo on a cardboard box like the motherboard box works just fine.
I use to run a few PCs without cases for shits and giggles a few years back. Never had an issue.