I think you're confused about how trading works. There is no "main price" for bitcoin. Each exchange has its own price that does not directly affect the prices on the other exchanges. I can put up a buy order for 1 bitcoin at $1,000,000,000 USD on Mt Gox and it will not affect the price on Bitstamp at all.
If you're wondering then why the exchanges have (generally) the same prices, look up "arbitrage." Basically if the price on one exchange is vastly different from another, people will move to that exchange and the prices will move towards each other (ex. gox last is 1000, bitstamp last is 5000, obviously I'm going to buy on gox and sell on bitstamp, therefore the gox price will increase and bitstamp price will decrease until they're about the same).
So to answer your original question, localbitcoins has no effect on any exchanges, and since localbitcoins is not an exchange it will have no effect on other localbitcoins orders. Plus, if you offer some ridiculous price on localbitcoins, people will know it's fake and ignore it anyway.
Also, you asked if someone with enough funds such as JPMorgan could manipulate the price (let's say on a single exchange such as gox). The answer is yes, but this is where the market cap comes into play. To significantly manipulate bitcoin's price you would need to be playing with tens of millions, maybe even a hundred million dollars, and even the riskiest investment bank is not going to do that. I remember seeing a 2 million dollar sell order a couple weeks ago and it did nothing to the market. Coins with smaller market caps can be manipulated easier but you still need to risk a lot of capital to try it. I understand the basic idea of how to do this but would be interested to hear more about it if anyone else wants to chime in.
I'm clear about how the exchanges work and about arbitrage now, after 12648430's (nice nick...) explaination, but thanks!
In regards to your last paragraph - tens and hundreds of million of dollars are no problem for the likes of JP Morgan, that's change for them, they probably spend more on fines for their manipulations every month.... the question is what could be their motive? Can't short BTCs... but for sure they will find another way to make money off it, or maybe the motivation could be to destroy BTC and help the fiat currencies...?