Considering that the app allows the phone interact with the car in more ways than just Bluetooth hands free & audio out - I'd say yes an app is needed so that the phone knows how to interpret the signals coming out of the car...

 

Connected is nice, but it's not essential. Both my wife and my MINI have it. Makes it easy to navigate ipod, and sat radio. Voice command is handy also (not sure if this already comes with non-Connected systems) and I like the look of the connected speedo better. I'm an Android user, but have an old iPhone that's permanent in the MINI to serve up songs, connects to the Galaxy S3 via hotspot and provides all functionality to MINI connected apps. You could do the same with an old G1 iPod touch. If you're looking where to spend your budget, I'd put connected at the bottom of the list. I think BT media streaming from any device is also only available through connected (non-connected systems allow phone, but not media). MINI connected apps don't have enough to justify the price of the system IMO.