If you don't want the sim to miss the birthday and be sad, then put the cheat code buff in to make the baby be born right away. ;)
Otherwise you could put the age span up for what the sim is by a few days so they give birth before, and don't miss their birthday and be sad.
Because the mod allows auto-aging up during pregnancy, it just means they or any NPC's will age up while pregnant. A sim cannot be modified manually with cheats or mods while pregnant just like without mods/cheats, so 'using the cake' is a manual way. That's why it doesn't work with a pregnant sim.
