The part of the file that gets downloaded over your data connection uses your data plan. The part that gets downloaded over wifi shouldn't (although I've heard of some carriers charging for wifi use, which is illegal - you can't charge for something you're not providing).
Download Booster is like the old download managers on Windows that used multiple download streams. It's nothing new, they're just using 2 different paths, their mobile data connection and your wifi connection to do the different connections. (Since the internet can only maintain about 2mbps per connection, if you use 5 streams - on wifi, mobile data, whatever - to download a file, you're downloading at a 10mbps thruput. It's the same as torrents, but fewer connections and faster servers. It's 1985 technology (RFC 959, page 30 [Restart]) with 2014 wrapping paper.)