Will tubeless tires out-perform my Armadillos on my commute?
Bald-ness isn't a problem on tires used on roads. In fact, it's favorable. I'd replace the tire once I start getting flats (or a bit before), or seeing canvas. 

The primary advantage of tubeless would let you run lower pressures (since you can't pinch flat a tube if it isn't there) which is useful for running big tires while mountain biking for more grip and comfort, but it won't really make a difference for commuting use (smaller tires at higher pressure). 

The best thing you can do is have a properly inflated tire and buy a durable tire (e.g. the Schwalbe Marathon line) -- low inflation can lead to rim damage and increased wear, while overly high inflation can also lead to damage, less comfort and loss of control. A properly inflated tire shouldn't see many flats in either case (road debris will be the primary cause , which sealant may protect against in the case of a tubeless tire). 

I'd stick with a tubed tire; tubes are relatively cheap and are easy to replace on the side of the road with slightly less mess than inserting a tube in a tubeless system. Note that you'll likely be paying a bit of money to go tubeless overall (e.g. with the Bontrager TLR kits).