This has come up before, and the answer is: Probably? Most likely not?
See, it's important to consider who Hemu was a general for. Hemu was a general in the Sur Empire of Sher Shah Suri, an Afghan nobleman in India. Afghans have been present in India since the time of the Ghaznavids, and they were an important part of the Delhi Sultanate. That sultanate, however, was brusquely shoved aside by Babur's Mughals after Panipat. The Afghans, weirdly enough, were viewed by themselves and others as "natives" since they'd been around for centuries, while the Turko-Mongols of Babur were "foreigners." All this set the stage for Suri's revolt against Humayun. He unseated Humayun and forced him to seek refuge in the Safavid court of Shah Tahmasp, and aimed to found a new Afghan dynasty. The first Suri's successor, Islam Shah, tapped Hemu for leadership.
In other words, Hemu rose to the top by pulling the levers on an Afghan machine, and staying at the top means making nice with the Afghans. When Hemu is ruling as the vizier of an Afghan Shah, that's manageable. When he's trying to found a new Hindu kingdom with himself as the Vikramaditya, that's really hard. One of the reasons why Islam Shah liked nominating Hindus to high office was to play them off the Afghan noblemen-- the two groups would keep each other in check by report each other's indiscretions to the Suri shahs. Therefore, if Hemu makes a power grab as head of the Hindus, he's going to have to reckon with the Afghans because they're already suspicious of him and his coreligionists. OTL, he died too fast for this to be an issue. But even if left alone by the Mughals (maybe the Safavids don't let them go or something) Hemu won't be able to rest easy. Maybe he allies with the Rajputs with a lucky marriage (if Akbar managed to do it, why couldn't Hemu?) and uses their help against Sur restorationists or other aspiring Afghan dynasty. Maybe he fails miserably while trying to do exactly that.