Answer:
A skimmer is not absolutely required, but you will have to spend a ridiculous amount of time/money to accomplish the same thing by other means. I cannot see how it would be possible to stock corals without one. The other advice is to get a good one as this and the lights are the two most important (and expensive) parts of the tank.
Another note - as the previous poster noted, there is almost no need for the fluvial filters in the current form. Remove the physical filtration medium and add something else, e.g. GFO, etc., to remove excess phosphates. Carbon can help too.