[C++][CI] Test the ported fuzzit integration image

[asfimport]

Reporter: Krisztian Szucs / @kszucs

Related issues:

• [CI][Crossbow] Fix or delete fuzzit jobs (is superceded by)

_{Note: This issue was originally created as ARROW-7141. Please see the migration documentation for further details.}

[asfimport]

Antoine Pitrou / @pitrou:
I think we're going to settle on OSS-Fuzz and not bother about fuzzit anymore.