ClickOnce deploy a Windows Service?

AFAIK you can't really use ClickOnce end-to-end to deploy a service; there are issues with both the file locations (ClickOnce installs into a user's profile) and installation (ClickOnce is largely side-effect free).

You can, however, write a service as an exe that can self-install/uninstall from the services list, like so; basically, you write it as as a console exe and handle some command line args, using AssemblyInstaller to [un]install from the current assembly. Another advantage is that the same approach can be used to help debugging, since you can run it from the command line.

I guess NO according to Choosing Between ClickOnce and Windows Installer

Instead of ClickOnce, I like to use the approach using Inno Setup, like in here https://stackoverflow.com/a/1450051/396200

You have more control over what and how will be copied and executed.

As Marc Gravell said in his answer, I create a exe that self install my service, and then use Inno Setup to pack and deploy it. After Inno setup installed, it automatically run the exe and then my exe install my service.