During WWII, Gandhi said that Indians should adopt a compromising attitude towards the British due to the stresses of war. Did this prolong the (near) inactivity of the Indian National Movement? Or did the economic and military losses suffered by Britain cause it to grant India Dominion Status a little earlier than it would have, without the war?
Its true that Gandhi did have a compromising attitude towards the British during WWII and even stated that
We do not seek independence out of Britain's ruin.
Reference: Transfer of Power in India by V.P. Menon.
Though Gandhi was the most influential figure in the political scenario at the time, it's important to remember that simply because he wanted to maintain a compromising attittude towards the British, many of the other political leaders (as you rightly pointed out, Subhas Bose) of the time did not wish to do so.
And this is clearly demonstrated by the active participation of the masses in the Quit India Movement. Though the movement was suppressed soon by the British, its success lay in the fact that the movement was not led by the usual political leaders such as Nehru and Gandhi, thus effectively proving to the British that Indian nationalism did not depend solely on leader such as Gandhi, but that even near ordinary citizens could keep the demand for independence alive.
Moreover, after the Quit India Movement was suppressed, Netaiji Subhas Chandra Bose continued the freedom struggle from outside the Indian borders through the INA, enlisting the aid of British enemies such as Germany and Japan.
So it's important to remember that the freedom struggle hadn't died out during the war, even though Gandhiji wanted to maintain a compromising attitude towards the British.
So, I would say that the war definitely accelerated the freedom movement. Along with the movements mentioned above, Britain was financially weakened by the huge war expenditure. Moreover, India no longer served as a valuable colony to Britain as the British had to incur huge expenditures on suppressing freedom movements and was unable to commercially profit from the colonizing India. And lastly, after WWII, Britain faced severe international pressure to begin decolonizing its colonies as it was hypocrisy on her part to fight against Japan for its imperialistic designs while she herself maintained such a huge empire.
Frankly, this is something that could be argued either way.
On the pro side, the war years did put a lot of other political activity on hold for the duration. The war also sucked up rather a lot of Indian manpower that might otherwise have been jobless and looking for something to do.
On the anti side, the crucial part played by Indian soldiery, and the self-confidence that had to have provided an entire generation, made independence pretty much certian at the end of the war. In fact, the war even moved British Government in 1942 to offer India full independence bost-bellum in exchange for full political cooperation. The offer was not taken up, but that's the kind of offer you can't really take off the table once its been placed there.
My guess is that World War II accelerated Indian independence. The proof is found that ALL of British colonies (except Hong Kong and Singapore) gained independence shortly thereafter.
World War II exposed the excesses of German and Japanese "colonialism" in Eastern Europe and East Asia. But it also highlighted the abuses of the milder versions of British and French colonalism.
World War II also destroyed the myth of British superiority. Even my (Chinese born) father was impressed when Japanese aviators sank the British battleships Prince of Wales and Repulse, and captured Singapore. (Not to the mention the successful attack on America's Pearl Harbor.)
Asians were also given a chance to prove themselves. A Chinese "counterinvasion" of Burma (Myanmar) in 1942 allowed the British Burma army escape destruction in that country, indirectly helping to protect India from Japanese invasion. The performance of "Asian" (Chinese, Burman, Indian) troops in the subsequent Allied counteroffensive in Burma did not go unnoticed in India.