Cade Massey and Richard Thaler say yes:
...we analyze the decision making of National Football League teams during their annual player draft. This is a domain in which incentives are exceedingly high and the opportunities for learning rich. It is also a domain in which multiple psychological factors suggest teams may overvalue the "right to choose" in the draft -- non-regressive predictions, overconfidence, the winner's curse and false consensus all suggest a bias in this direction. Using archival data on draft-day trades, player performance and compensation, we compare the market value of draft picks with the historical value of drafted players. We find that top draft picks are overvalued in a manner that is inconsistent with rational expectations and efficient markets and consistent with psychological research.
Here is the NBER link; here is a free version of the paper. Here is an article on the biggest NFL draft busts.
I haven't read through the entire paper yet, but I read through the introduction and parts of the discussion of the empirics. I was interested in how Massey and Thaler treated fan preferences for draft picks. They discuss it, but do not rigorously examine it. From page 34 of the free version of the paper:
A more subtle argument is that the utility to the team of signing a high draft pick is derived from something beyond on-field performance. a very exciting player, Michael Vick comes to mind, might help sell tickets and team paraphernelia even if he doesn't lead the team to many victories. We are skeptical of such arguments generally. Few football playerrs (Vick may be the only one) have the ability to bring in fans without producing wins. But, in any case, if high draft picks had more fan appeal, this shold show up in their 6th year contracts, and we find no evidence for it.
Fan preferences for draft picks matter. Suppose that the Vikings believe that player A, a linebacker, is the best player available in the draft that addresses what they see as the most pressing need. Suppose the fans *strongly* want the Vikings to draft player B, a standout collegiate wide receiver. If the Vikings do not draft B in favor of A, fans in attendance at the draft will roundly boo the choice and the Vikings will be "fanhandled" in the local media and on talk radio. These sorts of attacks affect teams (unless the GM and the coach like to be personally attacked and to be booed) at the margin and rational teams will account for them. If the Vikings draft player B, it will not be to generate fan interest but because of existing fan interest for the team. It's a sort of customer service. If you've ever worked in retail, you've no doubt heard that the "customer is always right." A rational retail manager must balance customer beliefs with his own.
If player B turns out to be a bust and player A turns out to be solid performer for another team, did the team act with irrational expectations? No. It may have very well acted with very rational expectations.