It might, but then again, the laws are relatively clear, which should limit the possibilities. Keep in mind, though, that I'm doing this off the top of my head. Nobody should take this as definitive and I'd ask anybody who's remotely interested to follow my logic and steps to make sure I haven't missed anything.
First, I'm making the perhaps naive assumption that these "Spirit sections" need their own copyrights. I admit that it's possible that it was copyrighted along with every paper that ran it, but that can't be the law since that would make it impossible to determine ownership.
Second, heading over to the GCD, we can look at "covers" for the newspaper inserts. Selecting a few arbitrarily, I see a couple of things. The title absolutely must be "The Spirit," because it's the only title indicated. Various "issues" do not carry a copyright notice at all, meaning that they were never protected--if it's stuffed inside, then it's not a valid notice. Those that do carry a copyright notice are credited to Everett Arnold. (I verified this as well with a scan I somehow have of one full insert--in that case, the notice is on the banner and names Arnold; that also confirms that there's no internal indicia. Hats off to Cimmerian for spreading that widely enough that even I have a copy without even knowing.)
Third, this should be a periodical, so I default back to my prior CCE check. The name of the series must be "The Spirit," and there aren't any listed.
Fourth, just in case, we spot-check a few years in books. I already did this with Eisner's name, since he probably would've been the person renewing the copyright, but checking a few years under Arnold's name can't hurt. And while I see stuff renewed from guys named Arnold as I check, none is "Busy."
Hopefully, if I've missed anything, someone will speak up, but I'm pretty sure that this covers all the possibilities. Unless Arnold and/or Eisner did something horrifyingly shady with regard to registrations or the Copyright Office systematically didn't bother to record their renewals, I'd have to say that this material is public domain across the board.
The only remaining tool I can think of would be to drop the Eisner estate a line, but my experience is that lawyers like to claim that the estate owns all and then remain bizarrely silent when there's no actual ownership. In other words, they'll tell you when there's money to take, but never confirm public domain status.
(Normally, I'd also suggest that the paranoid hire a copyright researcher in Washington to physically check the records, but that would imply--as I suggest above--an oversight consistently lasting through twelve years. While it's possible that ONE renewal slipped through the cracks, or even a season's worth, it's impossible that hundreds spread out over years would.)