If your parents are anything like my grandma, I think it would feel like a punch to the gut for them, so depending on how much you care about them, it could be a bad idea. If you don't have a good relationship with them, then it probably doesn't matter either way. How they interpret the message will depend on what their beliefs are. If they are fire and brimstone Christians, they will likely think that you are going to Hell, so if they care about you a lot, then it would feel like a double whammy. First they will lose you and then will have to deal with the fact that they think you're being tormented forever.
Writing suicide letters to people who don't understand the way we feel in the first place sounds so damn hard. When religion enters the equation, it makes things even more complicated. Good luck.