I am not familiar with Compsr but I looked at their website and based on what their minimum requirements:
- PHP 5.1 or higher, with GD2 support and Memory limit 64MB+
- MySQL 5.5.3 or higher
- Apache or IIS recommended
- 50MB of disk space
I think Composr should work on DreamHost shared hosting or VPS. Keep in mind that DreamHost has a money-back guarantee so you should be able to try running Composr first and see yourself if you’re satisfied.