It works with a PC who was saved from a PW to my local vault and when that same toon is saved again from a locally run module to the local vault. Just in case I am not describing this clearly, I just did this for two cases and I describe the process below.
As preamble, for anyone not familiar with with sequencer items, their scripts store the spell IDs of their spells locally on the sequencer item. That's why I was choosing a sequencer item for the test (and I have tested this with other items whose scripts store variables on the item as local variables). Also, there are standard NWN sequencer items (e.g. Isaac's Sequencer Robe, resref x2_sequencer3) that others can easily use to test this without even opening the Toolset.
First case: I have a toon on a server vault PW who has a sequencer item with a spell stored on it. On the PW, I save that character to my local vault, after putting the sequencer item into a magic bag in the toon's inventory. Then I open a module locally with that saved character. His sequencer item still has the spell stored. To be clear, the sequencer would have been blank (giving a "no spell stored" message) had I not put the item in a container before saving.
Second case: I have that same toon (same sequencer item with the same spell on it) in a module running locally and do the same thing - put his sequencer item in a bag in his inventory and save the character to the local vault - the same thing happens when I start a new module with that just-saved character. In other words, whether the character is saved from a server vault module to my local vault or from a local vault module to my local vault, the character's items keep their local variables if the items are put in a container in the PC's inventory before I save the character.