This makes sense from Ubuntu's perspective, and it will certainly be interesting to see the resulting data. I have a few concerns, but nothing insurmountable:
How will this affect downstreams? Downstreams/non-official-flavors may want to disable or remove any diagnostics. Keep them in mind when designing the implementation.
Users are not always installers. Will additional users be prompted of the diagnostics upon first login? Are these diagnostics intended to be system-wide or user-wide? If Ubuntu uses GNOME Initial Setup for new users, that would be a great place for this.