If that had occurred, what would have happened to the dollar?
Dollar actually went higher against most other currencies since the crisis unfolded and Treasury and Fed started pouring dollars to sustain liquidity... The reasons are that despite potential future inflationary pressures we are still in mostly deflationary environment; other governments are pouring their money (relative to their GDPs) as well; and relative safety of dollar-denominated investments created Treasuries bubble (which is just now starting to burst).
Since dollar is relative its movement can only be expressed and understood in relative terms. Similar to reason why price of gold didn't fall along with other metals (like platinum) but stayed about the same (due to "flight to safety" demand for physical gold).