[CI][Docs] Exercise documentation builds on the main branch

[asfimport]

We regularly have documentation build issues since the build has been disabled on github actions.

Reporter: Krisztian Szucs / @kszucs
Assignee: Krisztian Szucs / @kszucs

Related issues:

• [CI][Debian] rsync is missing (relates to)

PRs and other links:

• GitHub Pull Request #11567

_{Note: This issue was originally created as ARROW-14505. Please see the migration documentation for further details.}

[asfimport]

Krisztian Szucs / @kszucs:
Issue resolved by pull request 11567
#11567