Yes it would preclude hyperinflation. Of course, now we should ask ourselves what kind of situation results in the government having to spend more money into the economy than it is receiving back. Oh right, by not taxing those who have money. Money that doesn't circulate doesn't pay taxes. If you keep money in your bank account forever that money will never be taxed, the government will never see that money again. It must run a deficit, not because it is stupid, it must run a deficit because it is actively subsidizing an influential part of the economy and any refusal to pay the subsidy is harshly rejected not just by the rich but also by the poor.
The fact that inflation is the escape hatch for loss aversion psychology tells you that everyone on this planet is actively choosing for there to be inflation or even hyperinflation instead of a negative interest rate.
People will argue how immoral it is for a bank to tell you that your physical capital is slowly depreciating and thus even a 0% interest rate would be too high to offer to you. No, that would violate the principle of private property, private property of coupons that represent the time of other people, who are slowly aging and paying opportunity costs. People think they deserve to own the time of other people as if they were cattle or slaves. After all, their freedom to not be a debt slave violates your right to private property which is a far more pressing matter, after all the psychological bias of loss aversion justifies any hideous act (note how I didn't refer to immoral acts, as many hideous acts are considered moral).