In an emergency situation just after take off, is fuel dumping useful?

Imagine a hypothetical scenario where a jet heavily loaded with fuel experiences more than one engine failures after $V_{1}$. Then I suppose that losing some weight would be beneficial since the airplane is not designed to sustain climb with such limited thrust. In such a case a) how much would dumping fuel help in this emergency (i.e. is the rate of dumping fast enough?) and b) could the captain proceed to do it without ATC authorization if he/she considers it necessary?

• According to aviation.stackexchange.com/questions/8136/… 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. Moreover, in the situation you describe, I guess there'd be a fair chance that the plane will be back on the ground pretty quickly, and it might not want to land in a huge puddle of fuel. – Nate Eldredge Feb 6 '16 at 7:30
• You do not do it en.wikipedia.org/wiki/US_Airways_Flight_1549 – Trebia Project. Feb 6 '16 at 10:08
• If you are a twin jets you have bigger problem. – vasin1987 Feb 7 '16 at 10:14
• Clearly if it is an all engines out situation there will be no difference. I am refering to somehting like a 747 or MD-11 losing 2 engines. – user13363 Feb 19 '16 at 7:18
• You may instead elect to land overweight. A dual-engine failure is very rare and I would probably risk an overweight landing than waiting to discover the underlying cause in the air. – Hugh Jul 20 '16 at 5:53