This would result in lower tier managers announcing beforehand they claimed "x time for y project" and if the devs want their sickdays/bonuses/promotions they should claim same.
This would be anonymous, the only thing that wouldn't be anonymous is whether or not an employee has updated their survey within the last 2 weeks.
I would absolutely throw that hypothetical lower-tier manager you mentioned under the bus. The surveys could have a "rate your manager 1 to 10" question too.
I think it would be valuable insight to all levels of management. If the team is being death marched, happiness and quality surveys would drop. Or, if you see a team deliver a buggy project, but quality surveys were high all throughout development, then you could tell that the team was incompetent and hire/fire/train accordingly.
[0]: Don't ask people to guess completion dates, have them guess percent completed and then calculate completion dates in the software.