Under the Everett interpretation that's accepted by the majority of LW, there's no such thing as collapse. Here's an index of LW posts dealing with the topic.

Your question does have a valid rephrasing without the word "collapse", and the answer is kinda yes, you can't rule out the possibility of the gun firing. Quantum immortality is only the (controversial) idea that your consciousness cannot disappear completely, but you still end up horribly disfigured or brain-damaged with higher probability than get out unharmed.