I'm trying to write a program that collects the pedometer and heart rate data stream from the Microsoft Band 2. I've written an android app that does this but is it possible to do this without a smartphone and directly stream the data to a computer?
Yes, the Band SDK can be used with Windows Store 8.1 and Windows 10 Universal applications; you just Bluetooth-pair the Band to the PC and applications can stream sensor data from the Band just like their phone equivalents.
The Band SDK does not support OS X and I don't know whether it can be used in any arbitrary device running an Android-derived OS.