The short answer:
On Android: You can do this, but this may require special treatment for different vendors and/or OS versions. It won't be simple to support all (or at least most) devices, but with a lot of manual trial and error, it can be done.
On iOS: It's not possible locally, as Apple sees it as an invasion to the user's privacy.
The (slightly) longer explanation:
What is possible, for both iOS and Android, but will probably require a lot more work and external support than you originally planned, is to divert the calls via a server. This way, when someone calls you, the call is "stolen" by the server (which the user has to manually allow when installing the app) and the call is received on your device as a VOIP call, allowing the app (on the server side) full control over the call (which ones are actually received on the device, what's played, how long, recording, etc). You can see this app for an example of how it works: https://yallo.com/.
I hope this helps. Good Luck.
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