Yes. Both of them can live.
If you are male (haven't tried with a female), and still have Morrigan with your group before the last battle (she just has to be a playable character still, which means no killing her or kicking her out), she will offer you the chance to conceive a child with her and it will protect you from the taint. And, it will. Both Alistair and the main character survive in this scenario.