This is such a simple and great idea! Once the gratitude board is successful, I think it would be interesting to try to make it more personal and see how employees react to this. For example, each cubicle or desk having an area where post it notes can be left. Thus, employees can see who is appreciating them which in turn, will strengthen their relationship with other employees.
This is such an interesting perspective on expressing gratitude; gratitude can come from within and be expressed outward and still be a form of appreciation and really change the internal culture of a company. I think it would be beneficial to consider how management will respond to this added responsibility and how to communicate the importance of this idea. Perhaps you can present them with statistics on how gratitude increases quality of work and motivation.