From my understanding, in Europe, the chip and pin does make a connection. Terminals generally do have a connection. For a while a lot of them were GPRS or POTS, so you can guess how long this has been used. I remember a few restaurants that had horrible cell reception, and you were pretty much asked to come chip and pin at the counter where reception was acceptable.
I do think that below a certain threshold amount, making the connection isn't mandatory. That's usually when it goes quickly and it doesn't say "connecting". I've only seen it happen on small amounts. Do note, that this is what I conclude from the behaviour. It would be better if someone who actually knows how this works to chime in.
If anything, I do not think that it's the card that stores the transaction. It would not make any sense at all. Imagine I do a 1000€ purchase, and it would be store-on-card. At that point, I destroy the card or never use it again. My card never gets the chance to "synchronize" with anything. Now, perhaps I misunderstood what you meant with "the balance would be kept on the card", but it definitely doesn't involve storing anything on the card. It's the terminal that must store and forward the transaction. Granted, it doesn't change anything in your scenario, but given European chip 'n pin do connect, I doubt you attack would be feasible (ignoring the fact you need a 1000 unconnected terminals, which is doing to be very hard to find).