Prophet did recite quran for others, there is a reference to it in one hadees where he mentioned that Sura-e-fateha is sura-e-shifa also and can heal sick people. That shows recitation of quran can be used to help others.
Khatam is just a goal in Quran Khawani. You can read just one surat or few ayat and send the sawab to any deceased.