I contacted Vanguard with this question; they responded with:
All fund accounts that hold Admiral(tm) Shares are reviewed for eligibility
on an annual basis, typically in June. If any of your Admiral Shares fund
accounts have balances below the required level at the time of this review,
we will notify you by mail so that you'll have an opportunity to increase
the balance.
If a fund balance subsequently remains below the required minimum, we will
convert your account in that fund to Investor Shares.
Conversions are not a taxable event.
Your fund balance is solely determined by market value, so if the market value of your position in the fund is below the minimum threshold for Admiral shares (which is $10K or $50K, depending on the fund) when Vanguard reviews your account, they'll contact you. It doesn't matter if the decline in value occurred because you sold shares or because the market moved; Vanguard will still downgrade you if you don't top up your position.
In terms of taxes, if you sell shares in a non-tax-sheltered account, you may incur capital gains and will therefore pay taxes on that amount, but Vanguard themselves won't charge you any fees or penalties when they downgrade you.
One more note on the rest of your question. Remember that a mutual fund investment isn't as liquid as a savings account; you'll face a delay between selling your shares and the settlement of your funds, so in terms of liquidity, a mutual fund investment isn't a substitute for a savings account. You should always have an emergency fund that covers at least 3-6 months of living expenses set aside that is highly liquid, regardless of your other investments.
Also, you'll face much more volatility with an investment in an equity fund. For longer-term investments, this isn't necessarily a problem, but if you might need these funds for emergencies, you probably don't want to expose yourself to the risk that when you might need the funds when their value is at a low point.
