Is it safe to eat sugar-free foods while pregnant?

Safe. Sugar free foods are safe in pregnancy and with breastfeeding. As with many dietary concerns - moderation is key. You should have a well balanced diet through-out your pregnancy.
No extremes. Sugar free to a moderate amount is ok, but you really need more calories during you pregnancy. You have increased physiological needs and your baby needs calories too... So try to take appropriate amount of calories depending on how far along you are.