Yep, so really you have a "development" server where you get everything set up, then a "live" or "production" server where it's going to be running?
Yes, that shouldn't be a problem to do. Once you get everything running on your dev server, just FTP the files over to your live server, and export / import the database as well.
You may also need to do a couple little tweaks to the config files as well. (like changing database name / credentials and a few file paths type of stuff)