Answer
While ETC doesn't recommend setting up your networked system this way, this approach would work. The CueSpider Outstations contain what is essentially a small, unmanaged switch, so data both to the CueSpider and to the Net3 Gateway will pass, unimpeded.
Similarly, while ETC has not done any official testing, Tech Service mockups have shown that the POE draw through the CueSpider to a Gateway will not damage the CueSpider, or stop it from working.