Not if you mean: to have a local repo with two remotes (one GitHub and one bitpack).
You can define only one remote with this client, and it will be either GitHub or Bitbucket.
Yes, if you limit one remote, you can use GitHub for Windows with any upstream repo.
The process of adding an upstream repo is now easier with the (constantly) updated GitHub app for Windows :
select the url and then drag and drop text from your browser and drop it into the github app for windows. It will automatically add the repository.

(Original answer February 2013)
In order for GitHub for Windows to publish the publication (instead of "clicking on GitHub"), you need to define the remote " origin " (in the settings of your local repo) using the https address of the Bitbucket repository :
https://user@bitbucket.org/user/repo
So, if you create a local repo through "GitHub for Windows", you can add the right remote through its settings:

Please note that the first update will bring up the login screen so that you can enter your http credentials that you use on bitbucket.org: they will be cached (and encrypted) by GitHub for Windows throughout the current session.

(See " Password Caching" and " git: ' credential-cache ' is not a git command , for more on this credential caching mechanism recently introduced with git 1.7.9 +)
Any modification that you do locally will be picked up by the GitHub client for Windows (you may need to exit the repo (left arrow in the upper left corner of the GitHub click on Windows) and click again in the local Bitbucket repository: this will cause an update):

The key in the following screenshot is in the word " publish " (instead of " push to GitHub ").
This is because the remote "origin" is https.

Click "publish" and you will see that your repo status is set to " in sync ":

Rush to bitbucket.org to check if GitHub for Windows actually clicked Bitbucket:

VonC Dec 02 2018-12-12T00: 00Z
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