So let's suppose, if you have a grand total of 1 hp, and you cast prot spirit on yourself.. when you get hit by something, that attack damage will compute to 10% of 1 hp which is 0.1 hp, which gets rounded down to.... zero
Minimum damage you can take while prot spirit is on you (discounting the effects of armor) is 1, so yes, you will die. One interesting thing I have noticed though, is that it allways rounds DOWN to the nearest 10%. So, if you had a max HP of 19, you would still only take a maximum of 1 damage per hit.