I really think it does. I remember listening to a Bruce Arians interview (Head Coach of Arizona Cardinals in NFL) and he says he reads every single mock draft because he cannot help it but states that they are all very wrong and stupid. I remember when they drafted Logan Thomas he said "we really liked him, we also heard some teams behind us also really liked him so we were happy we got him."
When I went on my school interviews every single one asked how many interviews I have had previously. Even if they deny they do and tell themselves they don't think it I guarantee you they think "oh, he must be a really good candidate, he was in high demand since he got a lot of interviews" or "we are his only interview? damn we need to look at his application again."
Have you ever had a friend tell you some girl is hot who you didn't think was that hot? Even if you deny it, it makes you reconsider whether she is hot or not.
I know this makes me seem shallow but I am the only one to admit it.
Now back to GM's in NBA. If a NBA team really likes a player and the media and everyone else agrees with them don't you think the GM would be just a little bit more reassured? Even if it is the tiniest amount, it counts. It may not play a large impact and flip GM's boards over but everybody is human and this is a part of human nature.