If there are planets suitable for colonization in a sector, will the sector colonize them?
It appears to not be the case that a sector governor will actively colonize planets, at least in my experience since i had to build ships and send them on their way even if a sector had planets with 95% habitability.
It might be that case that they start doing that if you wait long enough (maybe the a.i. only settles on 100% habitable planets, i don't know) or chose a different focus for the sector but it certainly doesn't look like that's a likely scenario.
Also i think it's not even bad that sectors don't colonize new planets since the colony ships have rather high maintenance and if sectors would build them on their own it could ruin your economy which is something that players most certainly do not want. Besides, settling on planets could significantly raise your overall population count which can lead to extremely long research times for new technologies. I think both those things are the reason for sectors not colonizing, because it could really screw with your empire in unpredictable ways.