This reveals great confusion about how assets are priced and how treasuries are issued.
All of these treasuries are sold to primary dealers and the secondary market transactions are of little interest to any macro variable. Some treasuries are held by China in its Federal Reserve account. Should China sell the treasuries to another buyer, they will be transferred to a different account in the same bank. The nationality of the account holder makes no difference to the price of the asset.
The real issue is can China force the price of treasuries to be lower than it is? The answer to that is, maybe a little on the margin. Treasuries are priced as the expectation of average short term rates which are policy decisions by the Federal Reserve. So the real question is can China force the Federal Reserve to raise short term rates over a prolonged period? The Fed does this as part of an inflation fighting policy so this is a question about inflation and has nothing to do with China "dumping" anything.
Trying to guess the inflationary effects of something is hard, so I will throw out some theories and you can decide which one you like:
1. To the degree that US (and global) corporations have been outsourcing manufacturing to China to avoid paying higher wages to first world workers, then this results in driving down wage increases which could create an inflationary spiral, depending on your theory of inflation. Old school people thought inflation was the result of wages being too high. So if they are right, then yes, a very tight labor market could increase inflation more than expected and perhaps the Fed would need to keep rates a bit higher, but again to fight inflation, not because nation X no longer wants access to the US capital markets. I think most Americans would welcome this greatly, although stock prices would take a hit.
2. At the same time this would create an economic shock and the Fed may lower rates to stimulate the economy during the shock. So the short run effects are really mixed.
3. But there is another aspect here, which is that the trade deficit with China creates a loss of income for the US, which is made up for by increased government spending, whether disability payments to laid off workers, or welfare payments or other costs. Thus a reduction in the trade deficit will drive a reduction in the government deficit and thus a reduced demand to sell treasuries that moves in lockstep with the reduced demand to buy treasuries. So if you are of the newer school that says euler consumption trade offs are going to control investment demand, and sticky prices cause nominal interest rates to generate inflation, then once you adjust for the reduced government deficits created by trade deficits, you end up with a model that predicts higher short run rates and then stable long run rates.
4. There is the issue of international capital flows. Let's say we block China from purchasing dollar assets, so investment demand for the dollar decreases, therefore the dollar itself depreciates against the global basket, which causes US exports to be more competitive and we export more, which increases domestic income, which threatens an increase in inflation, which causes a small increase in rates as the economy is booming, up until the higher rates offset the depreciated dollar and things are back into equilibrium. This is why nations such as China intentionally devalue their dollar when they want to stimulate the economy.
Note that financial market beauty contests has zero impact on the US risk-free rates and thus on the price of treasuries. US treasuries are priced by arbitrage against the time path of future short rates, not by how popular the US is or whether some nation wants to hold treasuries.
You can pick among all of these or make your own scenario, but the bottom line is that rates go up only because the Fed raises rates in response to inflation. They do not go up because China decides to give away a bunch of its dollar assets.
China, of course, can sell the treasuries at a discount. Hell, they can give them away. That wont change the equilibrium price, it will just give windfalls to someone else at China's expense.
Capital markets are pretty elastic -- they will not run out of money to lend someone who is buyig treasuries from China on the cheap. Absolutely every bank will be willing to lend you money if you have treasuries as collateral, and the haircuts are small indeed. Hell, you can even borrow from the Fed itself to buy treasuries. Life-Pro Tip: If someone is offering to sell you treasuries at a discount, then buy them!
There will be no shortage of buyers ready and eager to relieve China of the burden of having treasuries.