Possible to run a GUI-less window's executable on iPad and/or Android Tablet?

If you mean Microsoft Windows, the answer is no.  Microsoft programs don't run on either of those platforms.

Please detail what exactly you are trying to do. A service component runs inthe background.
There are last time I looked an app for iPad that connects as an RDP session to a Windows platform and do .....

My exe should run in the background and it has a simple text-string communication protocol using sockets (but that might be replaced by something else if needed) — so it has no GUI — another App running on the tablet would implement a GUI and send messages to my exe which does computations.  It needs to read/write some files to the disk, so maybe I’d have to change that part?

I realize this might not be simple — just wondering how hard.  Another option: try to compile and build my MS C++ source code somehow for one of these platforms....?

You should start from what it is you are trying to achieve.
You could have an app on either that uses http/httpd requests to a service/web running on the Windows platform to perform and get what you need.

I have VMware and can run a perfectly emulated Mac on my PC -- and on a Mac "Parallels Desktop" let's you rerun any PC program on a Mac.  So..... I was hoping their might be something like that to run a windows program on Android or iOS -- and it's an easier problem, as there is no GUI in my case.

What does this application supposed to do?
you are mixing xapabilities of virtualization, VMware and parallels to apply to a completely different platform.
Look at whether VMware, parallels are made available for iOS and/or android.

The resources needed to facilitate the interaction that VMware/parallels provide would not be functional on the two platforms you are referencing.
Both apple and Google provide for an API through which you might be able to create an app to do what you want, instead of trying to fit a Windows service onto a platform for which it was not designed.

Yeah I get all that.  However, I do think it would be possible to build a virtual machine that ran on Android and could run a windows program.   Not saying easy, but possible.   They put a man on the moon... as they say.

My windows exe is 20 man-years of work, so "just rewrite as an App" is a possible solution - but before I go down that path, I thought I'd ask around just to be sure there wasn't some windows emulator that everyone one but me knew about!

Windows was the dominant platform ( a few years back. 90% of computers were windows ) and now its maybe Android that is winning -- you'd think that might create some market pressure to create tools to help migrate windows code to android.

WINE isn't going to help.  Tablets do not use Intel CPUs except for one or two.  iPads use Apple CPUs and most Android devices use ARM processors, neither of which is compatible with Intel CPUs.

much is now migrating to the Cloud available all the time and from anywhere.
Much depends on what this thing does converting this GUI-LESS component to run in the cloud and accessible from anywhere using any web interpreter.......

there have been many things that had 90% dominance at some point, until they were replaced by something different.

maybe you should consider creating a Web implementation that uses the service and exchange data between the web and the service.

It's already C++, so try to use Visual Studio (you probably need the Pro version):

https://www.visualstudio.com/vs/features/mobile-app-development/

After that, with a bit of tweaking, you can compile it for both iOS and Android.

@tullhead - the short answer to your question is NO - you CANNOT run ANY windows code on an iOS iPad or Android device.  Pure and simple .. there are NO WINE/VMWare or virtualisation options on either in the way that exists on Windows/ Apple OSX and Unix as they are completely different operating systems.

There is also NO such thing on iOS as a GUI-less app on iOS or Android .. again all 3rd party apps must be installed on the device and you cannot create a background services or load apps in the background or on startup on iOS (there are a few options on Android in terms of auto-launching apps, but no such thing as a background-only app or service)

HOWEVER .. it may be possible to recompile your code and build a simple app using software like Visual Studio and deploy that app for iOS and Android BUT .. a user will have to click on the app to launch it every time .. they can then let other apps take focus but in effect the app must be initiated by the user.

Another factor to bear in mind is that both Android and iOS implement a high level of SANDBOXING (on IOS it is VERY restrictive) which isolates all apps from each other and there are very strict limits on how apps can interact with each other.  Some data or information may be allowed such as shared access to private storage in each app but in many cases you may simply not be allowed or able to let one app share data or information with other apps on either Operating System.

In summary iOS and Android are a lot different from the standard desktop operating systems and coding apps for such environments is both complex and a lot more restrictive than standard Widows EXE applications

The Wine website mentions they are working on Android.   I'm not holding my breath, but I guess that's the best answer for the intended spirit of my question.  Thanks to all that took the time to comment.