They can and if they get the chance to they probably will. If you want them to survive, I would not advise putting fish that can fit into other fish's mouths together. It usually doesn't work, especially since corydoras fry are small and a gourami will see them as food(IMO).
I guess the next question is if they eat the eggs? I know I have to grab the eggs right away and even the cories will eat them. I have a separate 20G for they fry and babies...Only for them