There are ways to make the pump quieter, if that is your concern. If you don't need to run it continuously, for DOC uptake, I would turn it off in the daytime!
I used to turn off my skimmer at night for the very same reason. With my new tank and tunze skimmer i just turn it off after I feed any coral foods for a couple of hours as it is in the lounge I feel no need to turn it off.
If you have removed most of the DOC's from the water then O2 diffusion shouldnt be too pressing an issue, so you probably could, but quieting it somehow would be prefferable.