You can use it, but it does less damage and it always uses all of your energy so it's not worth using,

I think it's a good idea. I've played other games with sudden death periods and they add a whole new level of fun and intensity. 
You should post a topic here suggesting it!

I'm going to assume you're talking about the daily free rewards for the Tanki Birthday event. Correct me if I'm wrong, but I'm pretty sure this is the order:
Day 1: 12 Repair Kits Day 2: 12 Boosted Armors Day 3: 12 Boosted Damages Day 4: 12 Speed Boosts Day 5: 12 Mines Day 6: 12 Batteries Day 7: 12 Containers Day 8: 12 Ultra Containers Day 9: 12 Crystals Day 10: 12 Tankoins Day 11: 12 Mines Day 12: 12 Speed Boosts Day 13: ??? Day 14: ??? Day 15: ??? Day 16: ??? Day 17: ???

Ordinarily, you can complete that mission two ways: picking up the boxes or using your own supplies will contribute to completing that mission.
Since there are no supply boxes, you have to use your supplies.