"Demonic Spirit (Automatic): Although their origin may be shrouded in mystery, one fact that cannot be denied is that the Faceless have been tainted by demonic powers and owe their existence to it. As such, Faceless take x4 damage from sources of Psionic damage and this is considered a racial vulnerability. As with all racial vulnerabilities, Psionic damage will bypass any thresholds a Faceless might have. Also, Banish and Exorcism spells will not return a Faceless to their home plane but they will drop the Faceless into their Death Count akin to a Death effect. With the exception of these two special conditions, other Psionic effects function normally."
So could a faceless heal while using sigil of inversion?
Actually, Sigil of Inversion is a 1 use defence effectively, as it only converts the next hit to healing. As per the rules on racial disadvantages, single use defences against abilities that target your racials still work. In much the same way a Wood Fae could call a Magic Armor on an Iron Slay, I see no reason why a Faceless could not call Sigil of Inversion in this case.
Active PC's:
Tawgh, Firbolg savage and Aspirant of Zseria
Raven, Wild Elf of uncertain origins