I had a weird thought and I figured I'd ask to see if any astronomers on /sci/ wanted to comment on this. Despite being ridiculously improbable, could a habitable planet exist in a tidally-locked orbit around a close red dwarf and black hole (even if for a brief period in time, since the 3-body problem would probably complicate this very quickly and cause some kind of eccentricity in orbits)?

Also, if this kind of system, would the red dwarf appear to "shine" brighter than usual, since the Black hole was syphoning off its excess energy and forming a bright accretion disk?