I'm pretty sure the answer is no but everything I read simply says tapping into your first "Lightning Lane" unlocks the tier and park restrictions, without specifying that the tap in must be at a multi pass lightning lane.
It would be great if I could book my MP LLs at HS for the afternoon, and buy a SP for Avatar Flight of Passage for first thing in the morning and use that tap-in to modify one of the HS tier 2s into a tier 1, or to an AK attraction.
Great question