^Yes and no. Starting a new game sans 'Genesis' gives you a state where all the plot flags are basically set to null. So Wrex dies on Virmire, the council isn't saved, Shi'ala isn't spared, none of the sidequests are done etc. etc... I think the only exception is with the VS and who that is is determined by which gender you choose for Shepard. The result was fairly unbalanced towards the renegade end of things.
In ME3 they actually went through all the plot flags and hand picked all the different options to give a more balanced and deeper backstory for new players. That's why some ME2 squadmates are still alive while others aren't.