I fit a draft projection model along with by-coach random slopes and random intercepts in order to look into these ideas and wanted to share the data here. The intercept column show how much players coming out of that system tend to under/over-perform relative to other coaches. Each of the other columns gives the by-coach random slope for each statistic, telling us how much less/more informative each box-score statistic is when collected in a particular coach's system relative to others.
Here are all coaches in the data to produce at least 10 NBA players ordered by intercept:

I you want to pull the full data and play with it, I posted it to my Google-doc here: http://bit.ly/1jomLsR
I'm really interested if anyone can find patterns like "coaches running a 2-3 zone have relatively low steal slopes" that may help us understand how different systems impact our stats-based assessment of players.