First,

Just a reminder, that scroll that they gave us at Heidel Ball expires in 2 days

Second, that title question.  I dont really have a use for the scroll, but I have a life skill alt that I never did MSQ on. Was wondering if those twenty something inv slots that you get from the black spirit during MSQ transfer. I dont really want to test because the alt is 49, if the slots dont transfer Id lose 49 status for nothing 😬

I kind of expect it only transfers pearl shop stuff, but worth a shot to ask

At first I thought, well duh, of course it does.  Then it occurred to me that you could do the inventory quests on a character, transfer the slots to another character via the scroll, then do the inventory quests for that character, resulting in two sets of the sme quest-based inventory slots on one character.  And repeat if/when more scrolls appear in the future.  Doesn't seem OP though, so - why not? 

From the event page

* Using the Secret Scroll of Pure Equilibrium will also transfer the purchase history of Weight Limit purchases (Pearls and Loyalties) from the Pearl Shop (F3).

So my assumption would be no, as the quests are probably taken into account the same way as family history of bought weight increases.

Also a good point.  I'm not up to experimenting, an answer would be best.