Is the prayer of a congregant valid behind an imam who makes sounds such as "clearing his nose" and recites in an unclear voice to get past a point of forgetting in something other than Al-Fatiha?

The Sunnah (definition) is achieved by reciting something from the Qur’an after Al-Fatiha, and it is not a condition to recite a complete Surah (definition). So, if the Imam abandons reciting a Surah altogether, and limits himself to Al-Fatiha, his prayer is valid. And if the Imam lowers his voice during recitation such that his recitation is not clearly audible to you, this does not affect the validity of his prayer, nor the validity of the prayer of those who follow him.