The Sun's absolute magnitude (how bright it would appear at a distance of 10 parsecs), is about +4.83, which means that out to around 30 light years, it appears as a fifth magnitude star or brighter. Although there are many factors to how bright stars appear while observing from Earth, the classic constellations were limited to around fifth magnitude, or brighter (magnitude is an inverse scale; smaller numbers are brighter). So, for at least all systems out to around 10-12 parsecs, the Sun is bright enough to be included in their constellations (if they used the same criteria as our ancients did when creating star groupings).

Here is a chart of around 130 star systems where the Sun would be likely to appear as a significant constellation star.

http://www.icc.dur.ac.uk/~tt/Lectures/Galaxies/LocalGroup/Back/50lys.html