If an aircraft decompresses at altitude will everyone start farting?
No, they will not.

In the case of a rapid decompression, an aircraft will make a very rapid descent to a altitude, and while I'm not a physician or an expert on these physiological and biochemical processes, I doubt very much that would be enough time for dissolved gases to be released into the digestive tracts.

Even if it were, a person who experiences a sudden accumulation of gas in the gastrointestinal tract may experience discomfort or even pain, but it takes a while for gas to make its way to an exit - as anyone who has suffered from trapped wind will know.