That's one theory. A more accurate one is that Mad King George III was not so fanatical about shedding blood to impose his will as was Abraham Lincoln. King George acquiesced to their independence after having lost around 15,000 casualties. Lincoln would keep the war going until 750,000 people were dead.
England always could have ground the colonists into pulp, had they been determined to do so. They were simply more restrained than was Lincoln. Also the US had allies in the British Parliament (Edmund Burke) who weren't arrested and thrown in Jail for saying or writing things Lincoln didn't like.
May 18, 1864, the following order: “You will take possession by military force of the printing establishments of the New York World and Journal of Commerce … and prohibit any further publication thereof…. You are therefore commanded forthwith to arrest and imprison … the editors, proprietors and publishers of the aforementioned newspapers.”
That's not a theory at all but a fanciful interpretation of history. But say for the sake of argument King George had been willing to wage a far bloodier war. Do you truly doubt that the Founding Fathers would not have fought to the death to prevail? They were, after all, fighting for their liberty which seems to me to be a far greater motivator than fighting for slavery.