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
In this video from Mammoth Club, Molly says it has to be a multi pass tap-in to unlock: https://youtu.be/c741C4tCyjI?si=jWGKacOeNOHG24-d&t=4021
That would be a great little loophole (albeit an expensive one!) if it worked that way, I've a feeling it doesn't. Hopefully someone else will be able to confirm.