Yes, Dagger provides the core system API that allows creating and combining filesystem layers in any order you want. However it doesn't provide compatibility with existing package managers: that's something that you, or someone else in the Dagger community, would implement. You can extend the Dagger API with your own types and functions, then share them as reusable modules.
For example, here's a Dagger module for building Alpine Linux containers in an order-independent way. Under the hood it's derived from the 'apko' build tool created by the folks at Chainguard. https://daggerverse.dev/mod/github.com/dagger/dagger/modules...
And here's a Dagger Shell command for building a container using that module:
github.com/dagger/dagger/modules/alpine | container --packages=git,openssh,curl | terminal
You mentioned deb packages. Your intuition is correct, Dagger doesn't magically make .deb or .rpm packages reorderable, since those packaging systems are designed in a way that makes it difficult. But it does provide the primitives, and a cross-language programming environment for creating the "adaptors" you described in a way that maximizes reuse. If someone does for deb what Chainguard did for apk, you can trivially integrate that into a Dagger module.