A paranoid designer might indeed fake the appearance of a star, but
a straightforward approach results in the star's energy being
re-emitted from a solid surface (possibly one in many small pieces)
whose total area is vastly larger than that of the star. Thus the
energy flux emitted per unit area is much smaller than for the star,
the temperature of the emitter is vastly lower, and the spectrum is
substantially different. Thus a Dyson sphere whose diameter was 100
times its star's, would have surface area 10000 times its star's, and
temperature (via the Stefan-Boltzmann radiation law) ten times less.
Those stars for which we have been able to measure diameters
(either directly, with interferometers, or indirectly, by watching
eclipsing binaries or measuring spectral broadening and rotational
period, or by other means), have diameters in essence consistent
with just plain stars.
Furthermore, unless the energy is ultimately radiated at a lower
temperature than that of the original emitter, one cannot get much
useful work out of it as it goes by.
Of course, a Dyson-sphere designer might have designed a small
sphere, and have raised the temperature of the star inside it enough
to allow extraction of lots of work from the energy on the way out, or
merely faked a slightly cooler star than was actually present. But I
think present-day astronomy pretty well rules out the hypothesis that
a substantial fraction of stars are surrounded by large, "unstealthed"
Dyson spheres of the kind Dyson originally discussed (which more
nearly resembled dense swarms of asteroids than solid spheres, I
recall...). And if there are lots of spheres that are stealthed, I am
not sure I want to know what they are hiding from.
-- Jay Freeman, First Extropian Squirrel