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I think so. But also they lost even their case to make a trademark of it:

https://www.musicradar.com/news/guitars/fender-loses-guitar-...

https://ttabvue.uspto.gov/ttabvue/v?pno=91161403&pty=OPP&eno...

You would think this would have been quite an easy win, because regardless of who makes guitars with S-type bodies, the outline of the Stratocaster or Telecaster is surely sufficiently identifiable with Fender as to be something they could at least claim should be their trademark in certain categories (on merchandise etc.)

Fender failed to prove that if people saw a line art outline of the Stratocaster, they would associate it first with "Fender". And indeed an illustrated dictionary at the time used such an outline to just generically illustrate "Electric guitar", apparently.

And in that finding:

  Finally, there is no evidence of record that from the
  first production of the guitars incorporating these shapes
  in the early 1950s until 2003, that applicant or its
  predecessors in interest ever treated the outlines of the
  body shapes as trademarks. In fact, we may infer from the
  evidence of record that applicant and its predecessors
  themselves did not view them as trademarks. They never
  policed the body shape, only the word marks and headstock
  profiles. In addition, they never claimed trademark rights
  in the body outlines publicly through, for example, the
  catalogues, until 2004. Rather, they only claimed the word
  marks and the headstock profiles. In the meantime, many
  other guitar manufacturers sold guitars with the identical
  body shapes for at least 30 years, either as complete
  guitars or in the form of kits.

This was in 2009, when it was clear that Fender had never "policed" the body shape until that point.

And this — from a deposition from Warmoth as far as I can determine (they made spare parts) which makes it clear that Fender never entered into an agreement with Warmouth about the body shape, only the neck (because of the headstock shape which they believed was trademarked):

  Q. And you have a licensing agreement to
  manufacture what from Fender?
  A. Replacement necks utilizing the Fender
  trademark head shape.
  Q. In those discussions utilizing that license,
  was there any conversation or written
  documentation with reference to body shapes?
  A. No.
  Q. Would your company be harmed if you’re no
  longer able to make body shapes depicted in [126,
  928 and 127]?
  A. It would have a significant impact on our
  sales numbers and value [sic] of employees.
  Q. Why are you an opposer in this proceeding?
  A. I’ve been making these body shapes for 30
  years, unopposed, untrademarked, and have built a
  business on making these parts. There’s a lot of
  demand for it. While I make other body shapes,
  the demand for them is pretty insignificant when
  compared to these three shapes.

So this is Warmoth, in 2009, saying that Fender never asked them to license the body shape as far back as 1979 (which is also, if I remember reading correctly, when Schecter and G&L started making S-type guitars)

So even if they do have ownership of some kind of copyright, they've never asserted it before and three decades of their own conduct kind of militates against them being able to enforce it.

And they aren't the only ones, the finding goes on because Fender took action against multiple companies (this is around page 30–40 or so).