You can have advertising on your sites hosted here, but your paid upgrades will not transfer over. If the analogy helps, paying Starbucks for a Gold Card doesn’t get you and perks at another coffee shop.
WordPress has directions on how to move from .COM: http://en.support.wordpress.com/moving-a-blog/#moving-to-wordpress-org
If you have problems with it, I do recommend hiring them for the guided transfer. It works.