what are the chances that they would turn down a certified check for $200k from someone who has a few months to live?

In addition to the money, Alcor requires a lot of legal paperwork, including a notarized will. You can probably do that if you have "a few months," but it's one more thing to worry about, especially if you're dying of something that leaves you mentally impaired and makes legal consent complicated. I don't know how strict about this Alcor would be; I second the grandparent's advice to ask Diane.