There is merit to chelation therapy as a means of eliminating mercury (and other heavy metals including lead) stored in the body, but many protocols, both alternative and conventional, don't consider the full complexities involved and can be more harmful than beneficial.
There are a number of relevant factors including length of exposures (acute or chronic poisoning) and form of metal (organic, inorganic, metallic - for mercury at least).
By far the best source I found on the topic is Andrew Cutler, a chemistry PhD from Princeton who was mercury poisoned himself and created an effective and safe protocol for removal. He has a strong background in kinetics, pharmacokinetics, and biochemistry in general, and recognized that the standard toxicological protocols for heavy metal treatment were very dangerous (e.g. infrequent high dose IV administrations of DMPS/DMSA) , especially for cases of chronic poisoning.
According to Cutler, protocols such as the one you linked are very dangerous as they don't administer the chelating agent according to its metabolic half-life in the body (the half-lives of the chelating agents in cilantro and chlorella are unknown). As a result blood levels of the chelating agent and the metals fluctuate greatly. This can mobilize previously sequestered metals, but not provide the body enough time to properly eliminate them, which results in "re-poisoning" events. And when a large amount fat-loving free metals are released by the chelating agents within a short period of time, they often enter the central nervous system, settle there and exacerbate neurological symptoms.
I have no background in chemistry, so that's my summary of what I've read. But I highly recommend his book [1] which focuses mostly on mercury, but he covers lead as well. There are a few interviews with him around the web as well [2]. Also happy to provide more info and sources as I have two of his books and they both cite a wide array of sources.
[1] http://www.noamalgam.com/
[2] https://www.youtube.com/watch?v=J8AQGrh0XMw&t=34s