Back in 1998-2001, I know...a long, long time ago, I was the Schools Manager for Armor Branch at what was then called PERSCOM (now HRC). I worked side by side with the PDNCOs and Assignment Managers in Armor Branch. ASK had just come on board and it was a tool for the PDNCOs to use. From personal experience at the time, and I know it is a little dated, ASK entries were used in parts of the assignment process. An example would be when a PDNCO was looking for a Soldier to fill a specific assignment. I would get the assignment criteria from him...a certain rank, so much time on station, so much time in grade, any special skills required, etc...and their ASK choices. I would use a program called Data Query and I would scrub the ranks using the program. Once the data came back, I would package it into a spreadsheet and send it to the PDNCO. The way it works in the assignment process is the needs of the Army first, professional development of the Soldier and then preferences. If there was a Soldier who met the prerequisites for the assignment AND it was one of his ASK preferences, then it was a win-win. If not, then needs of the Army trumped.
Now that it just a specific example of how the ASK program was used. I am not sure if it is used that way now. There has already been some great responses with references to good communication with your PDNCO and I believe that nothing replaces that. Keep your ASK updated though. It can't hurt.