I wonder if anyone has tested this hypothesis by transmitting without any feedline (or conductive mast) at all ?
Yes, in various ways.
I spent over a day trying to get a 40m version to
show any sort of dip on an SWR analyzer,
Using something like an 18” jumper cable. Double
and triple checked every connection.
I gave it away to someone else who wanted to try
it, and they got the same results.
Others have reported the SWR varying as the coax
is rearranged, without any other changes to the
antenna itself. And adding a choke / current balun
at the antenna drove the SWR off scale, with no dip
anywhere close to the design frequency.
In fact, the manufacturer had specifically said NOT
to use a choke / balun with it.
But it isn’t unique in that regard - many of the claims
about small antennas have been found to rely on
radiation from the coax rather than from the antenna
itself. If you can mount it to a tower with a long enough
feedline, they may, in fact, be better than no antenna
at all, and get you on the air when it isn’t convenient
to put up a more effective antenna.