Yes, custom post types are supported.
Only WordPress custom post types are supported, though – some 3rd-party plugins use their own proprietary database tables.
Take a look at the ‘sample.csv’ file. You can try it out by changing the type from ‘post’ to your type in that file.
If that doesn’t help, please explain how you set up your custom type and send me a few lines of the input file (chrisvrichardson at mappresspro.com).