If you are talking about hooking up an oxygen tank to an airstone to add to the water then yes. If you over saturate the water with O2 then you can hurt your animals gills. If you are talking about adding an airstone then you will probably be okay, but you should test with a sample of your water (500mL or something) and run the airstone in the water sample for about 20-30 mins full blast, check your pH after that and see if the reduced CO2 levels have raised the pH more than you'd like.
Since my goal was to get a cycled tank I replaced one air pump with a water pump that on its end has this Eheim-Diffusor (thats how its is called in german) . My second airpump is still there and in use to run my skimmer. Right now I am not a home. Last time when I checked the PH I think it was around 7.
Do you have a sump? If so, consider putting anything that creates small bubbles in the sump and not in the main display. We have seen occasional problems with small bubbles ending up inside the mantle cavity and the octopus has no way to let that air exit.
If you are afraid that the tank is not cycled enough to handle the current resident then the best you can do is to increase your water change schedule. If you change out water once a week, then do the same amount twice a week. If you are only changing water out monthly (OK for some animals but NOT octopuses), then change to a weekly routine.