It depends on what you mean by a 'strong, centralized' Mughals. Mughal efficiency depended largely on two things: a) maintaining the Mughal's military superiority and control over the Indian military labor market (meaning foreign mansabdars as well as domestic seasonal/religious warbands), and b) making sure that the zamindars, the local landlords whom the Mughals depended for tax collection and basic admin work, did not get too autonomous.
Maintaining some modicum of religious tolerance was also important, but Aurangzeb's religious intolerance is generally overestimated as an issue of decline, and his policies more reflect increasing strains on the Mughal bureaucracy and the need to prioritize, rather than the rise of religious zealotry.
A) Control of the Indian military labor market - this was possible as long as the Mughals retained enough cash to soak up India's manpower pool, which could reach millions at peak season. The practice of handing out mansab to key foreign contingents was also critical in ensuring that only the Mughals had access to the best warriors; e.g. Rajputs (yes, Hindus served in Mughal armies), Central Asian cavalry.
Maintaining this system meant that the ability of the zamindars to re-appropriate income meant for mansabdars had to be curtailed, which Aurangzeb and his successors increasingly failed to do. The more long-term threat, however was the re-orientation of Indian warfare away from traditional massed cavalry tactics into infantry musket-and-drill formations, introduced by Europeans during the 1750s, which would have required a very powerful reform movement for the Mughals to adapt successfully.
B) Control of the zamindars - zamindars were in charge of tax-collection and administration throughout the Mughal Empire, and barring some massive revolution in how things were done I don't see how even the strongest Mughal administration would have changed this. Traditionally the Mughals suppressed zamindar influence (which unlike mansabdars were hereditary) by constantly touring around the country and shoring up royal power in the regions; as the Empire grew this became more and more difficult and Aurangzeb's decade-long stay in the south did not help things.
The establishment of a nationwide bureaucracy would no doubt be a step towards removing the power of the zamindars, but that comes with its own set of problems, not least in the fact that now the Mughals would face significant local dissent which would probably welcome any new invader that promised a change in governance.
A centralized, united Mughal India would definitely have been a stronger foil to the British, but it's difficult to conceive of a scenario where the Mughals attain that level of centralization. Ultimately that's not how the Mughals (or other Indian princes, for that matter) saw governance - they did not seek the destruction of alternative sources of power, but rather only desired their submission to the Emperor. And in a sense that means that their polities, while sprawling, were inevitably full of 'weak spots' that a colonial power on the cusp of industrialization could exploit to its benefit.