Does the Gradle IntelliJ plugin provide a way to publish to a custom plugin repository?

If you mean a custom hosted plugin repository as described in http://www.jetbrains.org/intellij/sdk/docs/basics/getting_started/update_plugins_format.html - no.

If you mean custom release channel, then yes, see http://www.jetbrains.org/intellij/sdk/docs/plugin_repository/custom_channels.html and "channels" property described in https://github.com/JetBrains/gradle-intellij-plugin/#publishing-dsl

I meant the custom hosted plugin repository.

Do you have a suggestion on how to do it for a custom hosted plugin repository?

I'm looking at doing the following since the Gradle IntelliJ plugin doesn't support my use case.

1. Run buildPlugin.
2. Upload the jar file created in the target/distribution folder.

You'll have to customize your build.gradle task to create proper updatePlugins.xml and then use FTP/SFTP/... tasks to upload the file. There's no ready-made solution.

Gotcha.

The zip file created in the target/distribution folder when buildPlugin task is run is the zip file that I need to upload to the custom hosted plugin repository right?

Yes, exactly

Yann Cebron: Is there any solution available for this now? Or for publishing it to custom repository, it need to be done manually only?

Also, by any means IDE dependency can be omitted to build plugin in Jenkins pipeline?

There is no automated solution for this.

What exactly do you mean with "IDE dependency"? You'll definitely need to setup the required IntelliJ SDK to compile against (which is trivial when using Gradle based setups, https://www.jetbrains.org/intellij/sdk/docs/tutorials/build_system.html)