That seems to conflate three issues: Did the League want independence? Did Muslims want independence? And did Muslims want the League? Going by the 1937 elections, the answer to the second and third would seem to be a clear No before the War. The first is more complex: Iqbal's defenders claim that his 1930 Allahabad address only sought a single Muslim-majority region within India, and his wording supports such an interpretation:

The principle of European democracy cannot be applied to India without recognising the fact of communal groups. The Muslim demand for the creation of a Muslim India within India is, therefore, perfectly justified.... I would like to see the Punjab, North-West Frontier Province, Sind and Baluchistan amalgamated into a single State. Self-government within the British Empire, or without the British Empire, the formation of a consolidated North-West Indian Muslim State appears to me to be the final destiny of the Muslims, at least of North-West India.... in view of India’s infinite variety in climates, races, languages, creeds and social systems, the creation of autonomous states based on the unity of language, race, history, religion and identity of economic interests, is the only possible way to secure a stable constitutional structure in India. (1)

So it's true that the League wasn't officially committed to separation until 1940. But Iqbal had also declared that "the problem of India is international and not national" and "there will be no peace in the country until the various peoples that constitute India are given opportunities of free self-development". Nor is it clear that a communally-defined Muslim state would long have seen its future as being within a wider India. The seeds of secession were already sown.