You would if you were running a protein skimmer
My skimmer doesn't use an airstone (AquaC Urchin), and neither does the author's, as he is using a Remora, as it says in his tank listing.
My water is aerated by the fall into my sump - when I built the sump I made the water enter into a "splash chamber" so that it aerates upon entry. It will then flow through a fuge with
Chaetomorpha I personally don't like the look of bubblers - not natural - but most people seem to, so I have one in my 90
gal FW to turn on when company comes (and at night, because my tank is heavily planted, and plants breathe at night, too). In my 55
gal cichlid tank I have one on all the time, because those guys are big, active, and produce
lots of waste - I want my bacteria to be stoked for that big load.
If you have adequate surface agitation and water movement you should be ok with gas exchange, but of course there are many other variables (bio load, macroalgae in sump or other refugium, etc.) which contribute to gas exchange.
Someone posted that bubbles have the potential to irritate certain inverts, but I'm not sure of this, so you may want to search it.
And then there is the infamous thread about the "farting clown trigger", which seemed to pass bubbles from its, well, you know... There was some discussion about whether a fish could ingest bubbles, or whether it simply ate Mexican food that night - a Mexican turbo snail, perhaps?
Good luck! Keep us posted on how you're doing, with or without bubbles.