If your alternator is charging, your voltage shouldn't drop when disconnecting the positive cable, and you won't get a voltage spike. If your alternator isn't charging, you can get a significant voltage drop, which can cause a spike and could endanger other components. The alternator is not a worry because it's already dead or the charging wire is broken. You would be more concerned about the ECM.
Running strictly on the alternator without the battery will provide a more erratic voltage. The battery acts as a buffer for the electrical system, smoothing out the voltage ripples produced by the rectifier.
On the favorable side, pretty much everything has spike protection, but your safety is not guaranteed. Try and get the cable off in one movement. If you get spastic and drag the terminal across the lug, sparking it, you can get voltage spikes.