Nah, it would just hurt their feelings and make them defensive. The only way for them to improve is to have a private heart to heart discussion about the ways they're being irritating, and if they genuinely listen and want to improve. If they're obstinate and think they're doing nothing wrong, unfortunately there's no practical way to change their mind.
We have something like this at work. It's called Bonusly. Everyone gets a certain amount of points each month, to gift to others. Accrued points can be redeemed for gift cards, travel vouchers etc. Ofcourse it's nothing but a popularity contest with absolutely zero to do with actual merit.
I feel like this puts the ‘service’ teams in a company at an advantage. Everyone notices when IT helps them with their problem – as is their job. But no-one will notice if the marketing team upped the sales by 20%. No-one notices the 50 emails HR had to send to their off-site payroll administrator to make sure employees would get paid this month.
Quite the reverse, in my opinion. Marketing is full with extroverts who love this type of thing, and that 20% sale increase is the only thing management will ever talk about (they get extra points to give away). While the quiet introverted programmer who keeps the company running at all gets nothing.
This would be very bad. Imagine if every employer could just go online and publicly badmouth every employee that ever quits or gets fired. It would be very heavily abused.
Employers would ban it immediately anyway because it could also be a tool for employees to evaluate each other's performance and be used for pay negotiations.