It turns out: No. You're thinking about it from only one side of the table.
For example: Gov'ts issue bonds on a regular basis to finance their debts. They depend on that market being there in order to continue normal operations. If liquidity evaporates, then many participants will not partake in the auctions, which is A Big Problem. Likely a central bank (a "lender of last resort") will step in for that case, but that only emphasizes that there are big market problems to the participants.
Opposite. Funds will flow to treasury auctions for two reasons. First, liquidity has to flow and will to the safest destiation; and second, account surplus countries (eg. China) have to recycle dollars to maintain their surplus and will have no options apart from treasuries.
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