Is Auto-Survey Worth Using?

Depends what you want to do and how many survey ships you have kicking around.  I find it's more useful to use the survey ship on manual at the start of the game, because it's good for scoping out star systems to find habitable planets.  If I can scoop up some rocks on the way, that's good too.

Later in the game when I'm looking for a research boost on a long project, I might direct one or two towards civ graveyards.

But yeah, auto survey is fine, it even seeks out anomalies in unexplored parts of the map.

Like Marvin says, it depends on what's most important at the moment however the big benefit of auto-survey is that the survey ships know where the anomalies and you don't so using auto-survey gets you more anomalies and sooner than you could do yourself.

The only down side of auto-survey is when you have multiple survey ships out they tend to clump up and become less effective but I find that if I see that happening or about to happen I shut off auto-survey for a turn or two and direct one of the survey ships away from the other for a turn before turning auto-survey back on.

One other thing to note about anomalies is that they come in a couple of varieties. There are anomalies that are apparently fixed when the game is created and no matter when they're surveyed they yield the same outcome. However there are a decent percentage (at least 10%) of anomalies that will give you different outcomes. Therefore I always save the game before checking an anomaly and then reload and try it again and if it changes then I can use the same technique until I get the result I want.