As long as you didn't format the Windows partition with NTFS, then yes, you should be able to simply drag it over. Unfortunately, you can't do the same the other way around, at least not without special software.
Parallels is different from Boot Camp. In Boot Camp, Windows simply does not recognize the OS X partition, so you can't really copy anything over if there's no place to copy things TO. OS X, on the other hand, DOES recognize the Windows partition, and thus, you can easily drag things over.