Web trees.
My answer is that the scope of a reasonably exhaustive research changes depending on what you're researching.
This was brought home to me by a piece I saw about whether a reasonably exhaustive includes DNA. (Answer: it depends.)
When you're searching, you want to get all the primary sources. Things like vital records, deeds, wills, censuses, military records, and civil and criminal cases.
You also want to look at all the standard secondary sources for the family and area that might contain other info. Things like published genealogies, county histories, lineage society applications, and research projects like the Great Migration Project.
When you're looking for secondary sources what you're really doing is looking to see if someone else has found other info. Maybe it would be something you missed because you didn't look in the right area. Or maybe it would be something not ever published, like a Bible record or personal memoirs.
So yes. I would think you'd normally check the major databases. My desktop program recommends 14 of the major "Lineage Linked Databases", including Geni, MyHeritage, FamilySearch, Wikitree, Ancestry, WeRelate, and Rootsweb.
But remember, this is all contextual. Web trees are good for scoping out your research but only if they might have good info. Great for 18th century Virginia, but if you're doing medieval research they're a snare for the innocent.