Yes and no. The drawer fronts can't be easily repaired, there isn't a good way to repair the broken corners. But they can be replaced and this shouldn't be terribly expensive.
The peeling laminate can be repaired. For this, the peeling and loose laminate is removed through hand scraping, a little sanding to knock down the edges, primer to seal the areas needing the repair and using either spackling paste or Bondo to build up the areas level with the surrounding undamaged areas. This is very doable.