Depends on what you call cheap. Japan was a particularly strong Omega market in the 1960s, and they appear to have looked after their nice vintage watches better than most, so you find a lot of 60s Constellations and Seamasters on sale from Japanese dealers.
However the Constellations in greater supply are the later C case models. There are plenty to choose from, and if you search well nice examples can be found at reasonable prices.
If you want a pie-pan dogleg Constellation it is a different story - prices are considerably higher for good examples, although still cheaper than some of the lunatic prices you can see elsewhere.
Like anywhere on the web, Japanese offerings also need to be carefully examined for redials. I have bought very nice watches from very trustworthy dealers there, but have seen a few online that were not quite right.
The Japanese dealers also tend to offer watches that have been polished: but to me, if the edges are still sharp and the observatory and surrounding machining is still sharp, I can live with it on a watch I particularly want. On the other hand, if the observatory is glossy and the stars rubbed, I won't touch it.
Japan is still a good hunting ground, but the number of really nice examples that come up seems to have diminished a lot over the least year or so.
