I cant see how the brake booster would be holding your brakes on.

I would think it would be more to do with an ABS module, the booster only helps you with pedal pressure force to the master cylinder, which in turn supplies fluid and pressure to your brakes via the abs module and lines etc.

However, having said that, if the booster is stuck, it would lock all the brakes, but it would need the engine running to supply the vacuum pressure.