I don't think so. As I understand it moving into a Money Market Fund means a bank can't loan out your deposit anymore. Think investing in a Vanguard Money Market Mutual Fund like VMFXX. Vanguard can't loan those funds out.
Yes it can, and that's the point of a money market fund. Money market funds invest in short-term debt securities. That's a mechanism for lending money.
Okay, let's be serious. This matches Keynes' liquidity trap. Unlike time preference theory which predicts that people will simply consume once the interest rate is below their time preference. According to liquidity preference people actually keep cash or short term assets, because interest doesn't compensate for delaying consumption, it compensates for going from a more certain and liquid asset to a less certain and less liquid asset near zero interest. So what happens instead is that there is a crowding out effect at the zero lower bound. You could think of it as if the private economy stops and the only thing left to do is for the government to micromanage things.
The only private market solution would be to get rid of cash and just let interest rates be negative. That way the crowding in effect that e.g. Austrian Economists predict when the government spends less money actually happens.
So yeah we are stuck in this situation where the private sector isn't credit worthy anymore and everything has to be threaded through the government. People rightfully complain but what exactly is supposed to happen? There are no answers left. Economists don't do money so they simply assume this situation never happens or resolves itself automatically.
The fund invests at least 99.5% of its total assets in cash, U.S. government securities, and/or repurchase agreements that are collateralized solely by U.S. government securities or cash (collectively, government securities).