Update Jan. 2023:
GitHub Desktop improves force pushing and fetching along with many great open source contributions (Jan. 2023)
GitHub Desktop 3.1.5 improves support for force pushing and fetching through the newly added
Repositorymenu items as well as supporting pull request notifications on forks.Previously, a user could only force push after an action such as rebasing.
Now, when users find their branch in any diverged state, they can opt to use the force push
Repositorymenu item.For example, a user can force push when commits exist on the remote that they are sure they want to overwrite.
Similarly, a user may find themselves in a new local branch they are not ready to publish, yet they want to fetch to see if there are any new changes on their main branch they would want to merge in.
Instead of having to switch branches, they can use theRepositorymenu item to fetch those changes.Learn more about GitHub Desktop here.
As of Nov. 2018, still no native support for a push --force in GitHub Desktop:
no mention of that feature in the Release Notes page,no mention in the current roadmap,issue 3580 was still pending.
That might change, considering GitHub is now displaying who did a push --force on GitHub.
Update August 2020, issue 3580 mentioned above now include this screenshot, by turtlemaster19:
Interestingly, in the Advanced preferences of GitHub Desktop (at least on Mac) there is this interesting checkbox:

