That's quite likely. Even when Huawei wanted to indicate that they've invented a completely new OS, with a Harmony-specific app format and everything, it turned out to be Android with the labels in the UI but nothing else filed off. Their new app format turned out to be a different extension and a few changes to make the files incompatible. India's attempt, if it ever starts*, will also recognize that there are a lot of Android smartphones in India and that you need app compatibility with those. They'll consider this problem and come up with three solutions:
1. Convince every developer to port to their new OS. This will probably be the government's position, and either some person will inform them that it's never going to happen or just change the specs so they don't have to try to make it happen.
2. Make their own custom OS with an Android compatibility manager, perhaps building it off the mobile Linux projects and something like Waydroid. This would be my favorite because we could take chunks of their stuff and include it in the existing mobile Linuxes, which are not very good right now but I'd like to see improve. It is also a lot of work for an OS the people won't buy, so I doubt they're going to waste their time doing it.
3. Why reinvent the wheel? Just use Android and call it something else. You wouldn't be the first, second, or ninth group to do that. Nobody would know except the technical writers who would write a full description of the OS a week after the first beta was leaked, but only other tech people will read that.
* I think what is most likely is that India makes a lot of noise about doing this and contacts a few places to begin work on their new project. A few months from now, they drop it after being told what actually doing it would cost and what the product would be like, change the spec so that someone makes a mobile app for something they want, call it by the same name, and then try not to mention it again.