Sure. Just FTP down to your hard drive your /wp-content folder which contains any themes and plugins you have. If you are running a later version of WP you can export your posts and settings to an XML file, set WP up on your new hosting account, IMPORT that XML file via the WP dashboard and upload your /wp-contents folders and files. You should be fine other than some possible tweaking of plugin settings (I had this happen with Contact 7 and a handful of other plugins when I moved WP that way last time).
You can either install WP manually on your new hosting account, which means you'll have to set up your database and database user yourself OR you can let Fantastico do it for you, if your host's cpanel supports that (most do). But I prefer doing things manually myself, less chance for glitches. :)