Yes. All you have to do is upload your files to us, which you can do via FTP or our control panel's file manager software. If you own your own domain already, you just change your nameservers (DNS) at your registrar (the place where you bought your domain) to ns1.unshadowed.net and ns2.unshadowed.net. Then you're all set.
If you have mySQL databases, you just export them to your computer and then import them via your control panel. If you have cPanel-based hosting already, it's even easier - just do a full backup of your site using cPanel, download it to your computer, and then restore it using cPanel on our server. Lastly, change your nameservers like we described above. If any of this sounds confusing, don't worry, we're always happy to help.