The battery has to have at least ~3V in order for the device to boot. The problem with using a smaller 1A charger is that that produces insufficient current to quickly charge the much larger iPad battery. So if you connect the small charger to a low-voltage battery like yours, no, the device will not boot.
You could leave it charged overnight to see if that gets the voltage back to where it should be (~4.2V) and then try to boot. Or get a proper 2A charger :>).