Releasy just uses Ocra on Windows, so it doesn't really do anything different - it just manages it at a higher level. You shouldn't be able to manage an SQLite database with Ocra (or releasy build:windows:standalone) since the database is extracted every time. If you use build:windows:folder or build:windows:installer, then you create a folder that can be used every time, so you wouldn't be re-creating the database every time you start the application.
I've never tried Releasy with Rails, but it should just work on both Windows and Mac fine.
As far as paths, you should use file-relative paths rather than cwd-relative paths to ensure you use the resources you expect to be using (and this is true in all Ruby applications, whether build into an exe or not).