Tenshinhan learned Kaio-ken? Sweet.
I don't think that the invisible Kaio-ken was ever a real thing. It's not like they were seeing Goku fight. I think that for us, the audience, the Kaio-ken was "invisible" for us to share the dead fighters' revelation that Goku was giving it his all.
And like all plot-based things in the series, we were told about it. I go by the simple rule of thumb that we have to go by what we're told. If we're not told something that isn't obvious, then it is "headcanon." If it's headcanon, then it's not real and isn't to be used seriously.
Edit: WTF--why's it look like this? Lol