Is there anything the skimmer filters that cannot be filtered by other means? I'm thinking of going skimmer-less myself.
There has been several studies over the years about this, where people would setup identical systems, but one was minus a skimmer. In pretty much all cases they found that coral growth actually improved slightly or was the same as the system with the skimmer. One such experiment was done my some of the guys in our sister group SCMAS, where he setup 3 tanks with identical corals, lights and fish in each, and each had a different filter setup. I'd have to look it up to see exactly what the filter setup was for each, but I believe he had one with a sump and skimmer, one without any sump or extra filtration, and one with a sump but no skimmer.
In the end he found that the control system without the sump and skimmer was stunted in growth, but the system with a sump but no skimmer seemed to grow corals at the same rate, if not a little faster, then the system with the skimmer. I've read a few articles too from some university studies and some other private studies that did about the same thing and got similar results, which in turn has encouraged me to try the experiment myself. Although at this point it is just that, an experiment and thus why I have included a chamber big enough to house a skimmer should I decide I need it.
Overall a skimmer provides 2 main functions, first is obviously it skims off excess proteins in the water, and the second is oxygenation of the water, and yes, both can be handled elsewhere by other filtration methods. With the proteins you can mostly handle this with increased surface agitation in the tank and the sump, which will keep it from accumulating on the top of the water, which would begin to block gas exchange if that occurs. Filter socks and filter pads can help filter some of it out as it flows into the sump, as well as live rock, and macros can also help absorb some of the excess proteins and convert to fuel as well.
My sump has a splash down chamber for the drain line. Basically the water will flow into the box at high speed, it will bubble and froth and the empty through a series of different micron filter socks before flowing into the large cryptic zone of the sump that is packed with rock, sponges, sea squirts and other filter feeders.
Just above the splash down chamber will be the 6" vent that will have an inline fan that will be pumping tons of fresh air into the chamber. This combined with the splash down of the fast moving water will readily mix in and promote oxygenation and proper gas exchange.
So a bit long winded but to answer your question, yes you can handle all the functions of the skimmer elsewhere in the setup, but you do need to compensate a bit to do so. As I see it the skimmer is kind of a convenience thing really, as it provides a few functions in one unit, where as with it, you need to handle those things through a series of other consideration.