Rosetta —> Intel Desktop app to iPadOS/iOS

No, that's not possible.
Rosetta doesn't in that way translate "an Intel Desktop app at install-time, to an Apple Silicon compatible app".
What it does is that it translates x86 CPU instructions to ARM CPU instructions, which means that it doesn't change the fact that it is a macOS app. It doesn't translate anything to a general Apple Silicon app, as that's not really a think.
It will still be a macOS app just like before, just that Rosetta will translate the CPU instructions to make it possible to run on this new (for macOS) CPU architecture that the app was not compiled for.

iOS apps will be able to run on the new Apple Silicon Macs because Apple has implemented specific support for that, not only because it will run on the the same CPU architecture. That is only part of it.

Besides the CPU instructions, the APIs must be available, Cocoa Touch and many other Frameworks had been added/shared to macOS, but not vice versa.

This is not possible with Rosetta 2 I'm afraid. As yingshen said, iPadOS APIs have been ported for Mac use. Catalyst will allow you to share code between an iPad and a Mac application, although this assumes you're starting with an iPad application not a Mac application.

Understood, totally makes sense. Thanks for all the quick replies!

I missed the (major) part of API usage, alongside the actual CPU instructions of an app.