No, just like App-V does not allow you to run 16-bit applications on 64-bit Windows, it also does not provide you with the means to run Windows applications on non-Windows operating systems such as Linux or Mac OS X. There are two reasons for this:
App-V does not provide any additional layers that applications can utilise at runtime. Providing APIs and other dependencies necessary for running Windows applications is the job of Windows itself – if the feature that the application expects is not offered by Windows, then you’ll have issue attempting to run that application via application virtualisation solutions including App-V.
Like other application virtualisation products such as Symantec SVS (and unlike VMware ThinApp), App-V virtualised applications require the presence a client. The App-V Client contains some kernel mode components so installing it on other operating systems would certainly be a challenge.
If you are looking to run Windows applications on non-Windows operating systems, then consider hardware virtualisation solutions such as VMware Fusion or Workstation, Oracle VirtualBox or Parallels Desktop, which can be used to run a virtual instance of Windows (and thus the App-V Client) on top of the other OS. Or if you’re looking to run Windows applications directly on Linux, Solaris or Mac OS X, then WINE is the way to go.