The anemone itself will not release toxins, (a debateable topic) however the ammonia spike from the decay of a large anemone will certainly have a negative impact on your tank (just as the decay of any other large creature would). If an anemone dies you need to remove and dispose of the carcass as soon as possible.
You would be able to expect an ammonia spike followed by the nitrIte spike, forcing you to do a good size water change. It also depends on what caused the anemone to die, could it have fired its nematocyst and are they still in the water column? or did it just have a meltdown from inproper lighting, water quality, or starvation?
My questions are if the anemone does not release toxins than how come I have read so many articles that talk about anemone toxins? If its not harmful to humans how about to the other inhabitants of my tank? (Thus I say the topic is debatable)
Thomas