Can Sims Vomit in The Sims FreePlay?

No. The Sims FreePlay does not have a vomiting animation or interaction. Sims can become "Nauseous" (from spoiled food, pregnancy, or illness), gaining a negative moodlet and needing the toilet more frequently, but they never visually vomit.

For more graphic biological functions, The Sims 4 (base game free) includes vomiting from the "Get Sick" moodlet (Seasons/Parenthood packs), and mods like WickedWhims or Basemental Drugs add further realism.