Skimmers remove proteins...waste products, junk in the water. Refugiums are great for keeping phosphate and nitrate levels down.
As for gas exchange, surface agitation takes care of oxygenating water, more so if you use an overflow and a sump.
Yes, skimmers remove foreign matter, including some supplements you dose. Some people just shut off the skimmer for a while when dosing, to allow time for these to settle in and be absorbed into the system.
Basically, the two remove different things. Thus, the combination of the two is ideal, IMO.