A quick analysis of over 3800 NFL games from 2008 to the present suggests that average depth of target (ADOT) is at best a poor predictor of football outcomes, with some evidence showing that higher ADOTs are associated with poor performance.
Of the 3804 games sampled, the team with the higher ADOT lost 1,970 of them, or ~ 52% of the time. A simple OLS regression shows that ADOT has a negative coefficient which is not statistically significant. When controlling for other more traditional passing statistics such as yards per attempt and completion percentage, the effect on points remains small, statistically not significant, and negative. Completion percentage and yards per attempt, on the other hand, have large and statistically significant impacts on points scored and point margins.
When other metrics of performance are used as dependent variables, the coefficients on ADOT tell a predictable story: that ADOT is associated with taking larger risks. Higher ADOTs are correlated with reductions in success rates and opportunities, as well as a sizable increase in the risk of throwing an interception. Every additional yard of ADOT is associated with an increase of .04 interceptions, which amounts to about a 5% increase in interceptions. However, these risks do come with a very small reward - namely that for every additional yard of ADOT, yards per play increases by .08 yards.
In the end, ADOT does not appear to be a meaningful indicator of performance. It suggests some small additional risks, with some very small additional reward in yards per play. That reward doesn't appear to be worth the additional risks, given the negative coefficients on ADOT in regressions with points and point margins as the dependent variable, as well as the overall losing record for teams with higher ADOTs.