If you export from Indesign to your "Cybergraphic" with convert colors turned on, your colors will transform to the destination profile, ie, heavy blacks will be mapped to blacks that your press can handle, if you then put it into prinergy with a "coated" profile it will more likely map them back to higher TAC blacks because of the paper profile.
My advice, let one or the other do the work, if you proof off the back end of your prinergy then let it do the conversion there, you shouldnt convert to uncoated then back to coated you will only clog up shadows and highlights from that type of conversion.
Run a couple of test rips yourself, make a grayscale wedge and a CMY gray wedge, do the conversions and see which ones you like the best.