I wholeheartedly believe that there isn't too much pressure on organizations getting the #1 overall right. Teams get it right far too often for there to be some kind of equivalent of the "reverse jinx" coming into play. Every single GM would LOVE the chance to get the #1 pick wrong...because they, to an individual or group, are certain that they are smart enough to get it right.
And I can't imagine how being drafted #1 overall is a psychological curse that would be mollified by the player being drafted #2 overall or any other selection. Who is feeling more pressure to perform a) the multi-millionaire teenager who has a big commitment from the parent club (D.L. Hall?) or b) a 23 year old right-handed college relief pitcher drafted in the 20th round (Scott Burke?)? Sure, Burke is getting paid...something...$1,100 per month? But I could find no proof of that. I'd prefer to take my chances in Hall's shoes.
Likewise, give me the #1 pick instead of the #2 pick all day, every day...
In his work, Jazayerli explains, "the value of a draft pick drops off rather steeply and consistently for the first 40 picks…and then flatlines." He adds, "As an interesting sidenote, in (Bill) James’ original study, he wrote that “players drafted #1 have produced about 8.5 times the major-league approximate value of those drafted #50.” In our study, the value of a player drafted #1 (46.37 WARP) was 7.2 times the average value of players drafted from #46 through #55 (6.44 WARP). The eras may have changed, and the metrics certainly have (the difference between Approximate Value and WARP is sort of like the difference between logarithm tables and Nate Silver’s supercomputer), but the relative numbers have remained reassuringly stable."
My take: #2 pick...very, very good. #1 pick...much, much better.