Good question. Unfortunately no, not yet. It's not context sensitive, actually it's as dumb as a brick:) If you enter the name of a table followed by a dot, it will offer only the columns from the table. Other than that, it offers pretty much all objects and filters them as you type.

I've been wanting to implement a SQL parser (at least for SQLite) so I can offer meaningful autocomplete, and some other nice features, but it was a lower priority than other things. I've done some work with Antlr a few years ago, but I'm itchin' to roll my own since I'm already dusting off my compiler theory books...

Anyway, why not give it a try, the trial is free:)