Everyone mourns differently. I don't feel it's inappropriate but personally I wouldn't want to post it since I prefer to mourn privately. There are many reasons to post though....to gain needed sympathy and support, to memorialize the loved one, to help oneself to accept it and other reasons. Also, it can help others who have experienced traumatic loss to relate and not feel alone in what they're going through.
Anyone posting should be careful though not to post too much personal info and consider also that there are trolls who enjoy posting mean replies.