Yes, and as soon as there is a bank run the bank stops giving people their money. Just like what will happen if everyone wants their tethers in USD at the same time.
"...but not regulated like any bank"
Tether is in fact not a bank, though? It is a service that in theory ports USD to block chains for ease of transaction. The last thing I would want for such a service would be to treat my money like it was a deposit at a non-FDIC insured investment bank.