Well, a lot of banks, insurance companies, trust funds, mutual funds, pension funds, social security funds, other countries and individuals own US treasury bonds.
China's holdings are significant - over $1.3tn or around 7.5% of all US government debt. If they were to dump all of it onto the market at once (a crazy idea which they would never do), the simple excess of supply over demand would cause Treasury prices to plunge and the USD would likely drop in the foreign exchange markets too.
As soon as someone at one of the big US investment banks realised what was going on, phone calls would start being made to wake people up in London and then New York (this assumes that the sell-off starts during Asian trading hours) and eventually someone would wake up Bill Dudley (head of the New York Fed). He, in turn, would wake up Bernanke and Lew, who would call the President (who'd probably already have been woken up by the IC/military).
By that point, the markets would be in turmoil. The combination of the sell-off with a big military move (i.e. declaring the South China Sea a closed zone) is interesting, because an increased likelihood of military conflict typically causes investors to sell riskier assets and buy less risky ones, like US Treasury bonds. So, stock markets would drop across the world - I'd say at least 3%, probably more like 5%. Buying gold and oil is like a bit of a kneejerk reaction in times of geopolitical turmoil, so those would probably rise.
I doubt the increased demand from investors for Treasuries would be enough to absorb $1.3tn worth of bonds so Treasury prices would be dropping through the floor. That introduces a new dynamic because Treasuries are commonly used as trading collateral, so you'd start seeing margin calls, just like we did during the credit crunch (which is what caused Lehman Brothers to collapse).
So, Dudley would almost certainly act to stabilise the market by instructing the Fed's trading desk to start buying Treasuries. I don't know what the practicalities are of the Fed buying $1.3tn at short notice (e.g. whether they can simply create that many dollars out of thin air and credit them to their counterparties' accounts) but, assuming they could, that would support the price of US Treasuries although yields would probably still end up jumping by at least 100 basis points, and the USD would probably drop significantly against the Euro.
So, all in all, I'd be inclined to disagree with the idea that China dumping US bonds would have absolutely no effect. :-)