This is statement from MS Blog
Inactive tasks will no longer be taken into account by the scheduling engine. Assignments to inactive tasks do not roll up to the task or resource summaries. Inactive task do not affect resource availability and will not be taken into account by Leveling. Baseline values that have already been taken are retained, but any new baselines taken will not include data for inactive tasks. Tasks with actuals cannot be inactivated.
Inactive tasks will appear in the Schedule WebPart on PWA, however they will be read-only. Inactive tasks are not published, so inactive task assignments will not appear on a team member’s task list.
This is the answer, tasks are published but just the task record with dates, not all the assignment stuff
Reading the part in yellow means they show up in pwa schedule view (means project center) and pwa only calls published db, the tasks are published and that is 100% sure. The red text must be read with some common sense in mind, they are speaking about tasks that show up in a person’s Task sheet in PWA. I put the first paragraph in there so you can see what data will not be published but the task its self will be published and show up in reports. The blog is not wrong just foggy.
The design around published = no is about the publish of assignment to users task sheet, this is a way to not pollute users pwa task sheets and to make it perform better but the task itself is still published so it shows in schedules so that PM can find it again and publish it when he needs to.