Yes, it is possible. When I received my nomination for the scholarship there was a section that explained how to request a change of assignment. I followed the instructions and emailed a Placement Division Officer, who then replied back pretty quickly. Unfortunately the unit I wanted to go to was full, and so then they put me on a waiting list.
On a similar subject, (sorry FR4Y, I don't mean to detract from your question) if your request for a transfer is denied, and your assignment is to a school you never applied to, and the deadline for the application has passed, what do you do?