Hazrat Ali most certainly had nothing to do with Sufism/Mysticism/Vaidant/Monasticism. He was Asadullah on battle-grounds.
In the Sufi thought and parlance, anything goes. "Khawja Hasan Basri" born 50 years after the shahadat of Hazrat Ali, claimed to be his disciple and the N2Is accepted him! All Sufi orders of today trace their origins to Hazrat Ali through Basri. If my memory serves me well, only the NAQSHBANDI Silsila connects itself to Hazrat Abu Bakr.