From memory you don't HAVE to do the research, but it helps to defeat the bosses. There are three of them: Blazer, Keller and Terron. Keller appears out of black holes - you can fight him in hyperspace (this is harder if you haven't done the research - you've been warned). The other two are in particular systems. If you want to win the game, you need to attack Dominator-controlled systems in search of Terron and Blazer.
Oh, and the research does carry over, but the stuff you bring only lasts a little while. You will need to bring lots of Dom stuff to get the research going at full speed.