Yes, but they can not exists if the percentage is say above 50% of deposits as then the less than 50% they have to loan will need more than double interest rates for any profit or covering the default rates. Only a tiny fraction of the 8 trillion would even come to the banks. - What of it they do get will not stay in the bank with ~10% of their current deposits going to the FED as they hope to lend it out again.Yes, banks ARE sponges that soak up a percentage of deposits as set by the government...the only question is to what degree.
Also you are forgetting about the multiplier effect - i.e. every dollar deposited (with current 10% reserve requirement) makes up to 10 dollars circulating. Thus if even 1 trillion of the thin air dollars did come to the banks it would add about 8 trillion more (multiplier effect dollars) to the 7 trillion circulating that never came to any bank.
You seem to think that banks don´t lend, just take in deposits so the amount they must send to the FED would grow with time until most of the 8 Trillion of paid out would come back to the FED. It won´t as banks lend out most of what they get as deposit, - They don´t just keep sending it to the FED.