In an emergency situation just after take off, is fuel dumping useful?
You would not attempt this. Aircraft are certified to climb with engines inoperative after V1, they would just climb to a holding altitude and run the checklist. They would rather not attempt to any cruise altitude. Running the checklist you would determine if you are above the maximum landing weight (MLW) and decide to burn or if able, to dump fuel.

Dumping fuel during the takeoff/rotation phase is not advisable to be honest, as you would leave a contaminated runway behind. Sure, most of the fuel will evaporate, but there will be a contamination nonetheless.

I will quote Nate Eldredge's comment shamelessly for another item to consider:


  According to How is fuel dumped in aircraft? a 747 can dump 6000 pounds of fuel per minute. Given that (from what I found) it typically carries at least 200,000 pounds, and has an MTOW of over 800,000 pounds, it seems unlikely you'd dump enough fuel fast enough to make any difference.