Is it possible do apt-get install using ZPM?

Short answer: yes, ZPM can manage whatever you want other than ObjectScript, it just takes a little extra work.

Longer answer:

This "extra work" involves writing a class that extends %ZPM.PackageManager.Developer.Processor.Abstract and overrides OnBeforePhase or OnAfterPhase, then implementing whatever behavior you want. You can see a bunch of classes in the %ZPM.PackageManager.Developer.Processor package that do this.

I'd imagine being able to put something in the Resources element of module.xml like:

<Resource Name="/external-dependencies/some-package" ProcessorClass="MyPackage.AptGetInstall" />

Where MyPackage.AptGetInstall overrides OnAfterPhase and for the "Activate" phase runs apt-get install <name of resource following "/external-dependencies/"

The catch:

If you want to support all operating systems, think about what the Windows equivalent would be and/or add defensive coding to avoid trying to run the command on Windows.