Assuming that you have a standard 68mm BB, there will be a 2.5mm spacer behind each bearing holder, which you chuck away. That gets you a possible 5mm gap between the pedal arm and the BB, but the sensor bracket takes 1mm and the magnet disc is about 6mm thick, so you end up with just enough room to get the pedal arm on. You only need to pull the pedal arm against the magnet disc, it doesn't need any clamping force, but the plastic threaded piece that goes in the spindle pulls everything in the BB together.
If you have a 73mm BB, this method won't work.