Matthew - welcome to the forum!!!
I looked and that is the basic set they have at Wal Mart... the airbrush would work ok for all over coverage but would be less than adequate for finer detail. If you did nothing but armor and such it might fit your needs but for most military aircraft it would be a bit lacking. Also it is plastic so I am not sure how it would handle some of the stronger hobby paints (lacquer etc..)
What model Badger do you have? For about $69.00 you can get a commercial style compressor at Wal MArt or Lowes and they already come with a pressure gauge which would help in your spraying. Most badgers would hook right up to it with an additional brass 1/4 to 1/4 inch adaptor available in the compressor section for about a dollar. The only Badger that wouldn't hook up to off the top of my head is the 350 external mix, it would require a special adapter to get it to work. Probably a 1/4 to 1/8 adaptor.
If noise is an issue (the commercial compressors are a bit loud to some) then at www.badger-airbrush.com in the garage sale section they have a Thayer and Chandler compressor for hobbies specifically. Same with this, it would hook up to most Badgers right away and it is somewhat quieter. I think it is about $90.00.
If cost is an issue I would think about saving more money for a better compressor. If you are an occasional modeler that doesn't spray a lot of fine detail the brush would be ok but If you foresee more use out of it than occasional I would stick with your Badger..
---edit---
oh yeah...unless your Badger is the 350 it looks like it won't fit on that compressor...