There are no stupid questions, only stupid answers!
Onto your question. The Logitech has an excellent interface if you ask me, superb in fact. If I may suggest you to post the rest of info about your system as DACs in general are not always the best thing to upgrade if there are other 'burining issues' with the system. Unless your heart (and mind) is already set on a new DAC, perhaps some other upgrade would be more worthy.
Using the AES (short for Audio Engineering Society) balanced XLR connection would work beautifully with your Logitech. Just remember to use a proper 110 Ohm characteristic impedance cable to connect the two. Don't spend too much on the cable – anything made with a Belden 1800F cable and Neutrik XLR connectors will work as good as anything else.
I assume you're interested in the BDA-3 but regardless, Bryston DACs generally sound excellent with the AES connection and electrical (S/PDIF) connection in general. They have impedance-matching transformers on each input which they don't really advertise but it certainly isn't a common feature in the world of DACs.
All of that being said, only you can decide whether a new DAC is worth the cost. It will be dependent on your 'ear' – whether you can hear the actual difference, number of inputs that you need, the style of the piece or how it makes you feel. People tend to think of upgrading DACs as if they're upgrading a cartridge on their turntable but in reality, it doesn't really work that way and though I'm sure you'll read otherwise, I will be the first to tell you that even a relatively affordable DAC can sound excellent.
Hope this helps. Cheers – Antun