It should work, but occasionally, it might go wrong, because a certain TC number gets hit or not.
Another option would be to just capture the entire tapes, and assign them the right tapename. This means you would have to allow the Avid to see tape names from other projects, and then you would need to select the exact right tape that was created in the older project.
After that, the sequences should (re-)link to that footage. Probably best to work with copies.