Is so-called Planet Nine (given it exists) observable in principle? By "observable in principle", I mean "if we knew exactly where to look, would we be able (from a technological standpoint) to get an image of the purported celestial body"?
If they knew exactly where to point Mr. Hubble, then yes, it should be easily visible, though at that distance, it would still be blurry, not a clean image.
Hubble can see things up to apparent magnitudes of about 30, so, yes, it should be easily visible by Hubble or (perhaps) even more visible by an infra-red telescope or radio telescope that knows where to look. But in any case, with current technology all images would still be blurry. Hubble's pictures of Pluto are blurry and Pluto's much closer.
Of course; how would we find it otherwise? This is how we look for it: image one part of the sky with a telescope, about where the planet is presumed. At another time we image the same part again and see whether a star moved or is no longer there. This star is the wandering star = planet we're looking for.
The hypothetical object has a very elliptical orbit, and perhaps can even be seen with the naked eye when at perihelion since it may be a primordial black hole (which itself isn't visible but its accretion disc would be). About 4,000 years ago, when the black hole (if it is one) was closer to perihelion, the Sumerians may have seen it and called it Nibiru. But we dunno whether that's the currently looked-for Planet IX.