Can elves die by being poisined???

I always thought that Elves could die from poisons which would kill a mortal outright, aka very strong ones. But I do have another question: The deaths on the Helkaraxe, could they have been partially due to grief as well? I mean, could they not have grieved for the deaths the Noldor caused in Alqualonde and, for example, the ice Elenwe and Itarille for buried under just being the right 'situation' for Elenwe's fea to attempt flight?