In reply to Baz P:
I've only ever used it to connect myself to the anchor while I rethread, or while setting up an abseil. I wouldn't want to use it for my principal belay anchor as I would worry (perhaps unnecessarily) about the friction device slipping under the loading if I had to hold a leader fall. I would always use the climbing rope for that, although perhaps keep the Connect on as well. I'd then probably tie off the slider with a couple of half hitches, but I'm paranoid.
I can't see it functioning any differently on trad anchors, but why bother? As midgen pointed out, it's an extra bit of clutter on your harness, which is probably already more cluttered than when on a sport climb. It has only one purpose, and that purpose can just as easily and quickly be achieved using gear you'll be carrying anyway. Unlike a sports climb, you shouldn't be untying from the climbing rope so you don't need an independent anchor.