just tested it with my spare mmc card, first file read only, deleted fine over AS, it did popup a warning saying that it is read only, second file system file, would not delete, third file read only + system file, would not delete.
the message it gives is
Cannot delete file test3: Access is denied.
Make sure you mobile device has sufficient memory, that the file is not set as read-only, and that you have permission to copy this file type.
the remaining 2 test files were deleted fine using file explorer on the device itself.
Hope that helps.