Yes calcium chloride can and usually will kill plants if you get enough of the calcium chloride on or around the plants.
So I would avoid using anything that has calcium chloride around plants.
For example the ice melt that contains calcium chloride should not be spread around or near plants because the plants could die as a result of the calcium chloride.
I used some calcium chloride based ice melt and got some on my plants around the house and the plants died within a few weeks of doing so.
Also I got some ice melt with calcium chloride on my grass and the grass in that spot died as well.