Hi! Just as MrNobodyWTB said. As long as you have available ingots (regardless if you recharged it during the event cycle or before), you will be able to participate in Naruto's Froggy. The reason is because the requirement of Naruto's Froggy to participate is to "participate" in the event by "depositing/spending" the ingots.

This is different from "Platinum Monthly Card" because that one has a specific requirement as shown below:

Either you need to have recharged 300 ingots or more on the same day you would like to purchase the Platinum Monthly Card or to have a Jonin Medal.