I don't think it would make a huge amount of difference, to be honest. How many features are you reading in?
If you want to give it a try, most of the database readers offer a "SELECT clause" option in the reader properties, where you can write your own selection.
If you're experiencing performance problems, I'd normally look at fine-tuning the writers first - your first writer is written on the fly, and some formats are relatively slow by default.
Just use an "attribut keeper" after the reader and keep nothing. so all your Feature will have no attributes...
You could try the FeatureReader transformer. It has an 'attributes to expose' parameter. I don't think it would stop FME reading unwanted attributes from the start, but it's possible.
If it's data in a database (rather than a file Geodatabase) I suspect you could use a SQLCreator transformer to read in just the geometry column, and then a GeometryReplacer transformer to turn it into a proper feature. But I'm not certain it would work (will the GeometryReplacer recognize the geometry field content?) and you'd be bypassing a lot of probably useful functionality in the Esri Readers.
But really, those are just hunches. I can't think of a way to do this with a setting proper. As @rollo said, if you have performance issues then do check your entire translation. Usually the reading part is the least problematic.