We ran tanks for years before the advent and wide spread usage of skimmers. It can be done. IMHO, you will not really be able to care for SPS corals. One of the reasons we can now is because of the technology that has come along in filtration and skimming. Also, if you are going to go skimmerless and want a reef tank, you can not just it half-way. The system needs to be planned out around not having a skimmer. You need to have a large amount of LR, good bio-load, good clean up crew, etc. Also, there are downsides to using that bio-wheel, make sure you know about them.
But short answer is that it can be done!