Dear god, no...
The Hittites would certainly become the hegemonic power in Syria and the Levant, with Egyptian power potentially shrinking all the way back to Sharuhen (near the modern Egyptian - Israeli border). However, the Hittites simply do not have the logistical power at the time to invade and conquer Egypt, which is protected by both natural barriers quite foreign to the Hittites, and a sophisticated fortification system. Additionally, the Hittites may also be plagued by internal troubles in short order (the Hittite court was a viper's nest of intrigue at the time), further hampering their ability to invade Egypt.
Also, Egypt would not simply roll over after a defeat at Kadesh. It would be wounded, of that there's no doubt, but it wouldn't be rendered incapable. It is also far more stable than Hatti at the time, as Ramesses II (despite being young, though not quite as young as people seem to think) had several sons who were both old enough and capable enough to step up in the event of his death at Kadesh.
Whoever ends up ruling Egypt may lead a counteroffensive to limit the Hittite gains. They probably won't be able to do much - the Hittites could extend their border as far south as Sharuhen, as I already mentioned, and the best the Egyptians could probably hope for is pushing them back to the area around Jerusalem/Megiddo. If not, the Egyptians will simply retreat inward and lick their wounds, and possibly emerge a generation or two later with a vengeance when the Hittites may or may not be suffering from growing pains and internal strife.