I think they can be effective. I worked as a physical therapist pre-kids (but mostly in early intervention where we don't really use TENS).
As you said, the theory goes back to the "gate control" theory of pain relief. Basically pain travels on a different track through your spinal cord than other sensations. The "other" sensations (like the prickly feeling tens can produce) travel *faster* than pain signals in general. So essentially the TENS confuses your brain because that signal is traveling up your spinal cord faster than pain and it kind of interferes a bit with how your brain is processing the "pain" signals.
FWIW, this is why certain things like "mineral ice" etc. work...the "tingly" sensation they produce is sort of like a more mild version of TENS.
Sometimes you can almost create a bit of an acupuncture-like effect with TENS as well.
I haven't used it in labor but have considered it. Hypnobirthing/hypnobabies did the trick the last two times, but it never hurts to have extra options available
eta: some people find the "prickly" sensation from TENS really annoying, some people aren't bothered by it. Not sure if you got to try it out in advance. and you are right...Transcutaneous Electrical Nerve Stimulation
Not sure if there's anything else you want to know...you seem like you understand it pretty well already, but ask away if you have any questions.