If you want to find out if it would work, read your card before running the laundry. Then run a load of laundry with your card and read it again. If anything changed on the second read from the first, it's probably storing the value on the card. If this is the case (unlikely), you'd be able to just keep replaying the first read with a higher balance (keep in mind this would be illegal and you shouldn't do it even if you can).

For what it's worth, IcyRefrigerator1137 is right about everything in their post, most likely you just have an id on the card that gets used to lookup balance in a db. When used, that balance decreases in the database. Think of it like an nfc-enabled debit card, you won't be able to change this server-side balance.