Dany Heatley - 2nd overall in 2000 in his 2nd year of eligibility
Maybe some caveats with the NCAA guys like Heatley in the 1995-2004 range since players had to formally opt into the draft. To maintain their college eligibility, those guys had to wait an extra year before being drafted. This led to a few guys being ranked on Central Scouting's list presumably before they committed to college.
In the same draft year as Heatley, Rick DiPietro gave up his college eligibility instead of waiting until 2001.
Another example was Mike Van Ryn being 56th on Central's final ranking for North Americans in 1997. But since he played for Michigan in 1997-98, he had to wait a year before entering the draft (and was drafted in the 1st in 1998).
And then there was the odd case with WHL prospect Adrian Foster who decided not to opt into the 2000 Draft because he missed most of his original draft year due to injury. Foster was a highly regarded prospect and was the 3rd overall pick in the 1997 WHL Draft. He had been on teams with Dany Heatley + Krys Kolanos and put up comparable numbers. By 2001, Heatley and Kolanos were tearing up the NCAA.
ELCs weren't as regulated back then, so there was some financial incentive to get drafted higher. Foster would have another injury plagued year but opted into the 2001 Draft where the Devils took a gamble that he'd regain the form when he was younger. Apparently a few teams had indicated to Foster that they were ready to draft him on the first day (rounds 1-3).
I forget if Travis Zajac opted into the 2003 Draft or if his plan was always to go to North Dakota/NCAA. He probably wasn't on too many scouts' radars in 2003 but then doubled his offensive output in the BCHL and ended up in the 1st round in 2004.
Not a first rounder, but Wayne Simmonds went undrafted in 2006. Owen Sound GM Mike Futa convinced Simmonds to give up an NCAA scholarship to Bowling Green to play in the OHL. Meanwhile Futa was hired by the Kings early into the 2006-07 season. Simmonds was not listed among Central Scouting's top 210 for North Americans in 2007. He said his only pre-draft interviews were with Atlanta and New Jersey, so he expected either of them to take him with a late round pick.
But since Futa was well connected with Simmonds, LA didn't need to do any extra background work. Originally they were going to draft him at #52 but the table was surprised that Oscar Moller (THN #19, ISS #24) was dropping. Presumably LA had Simmonds ranked over Moller, so the table huddled and debated whether to take Moller first since it was unlikely he'd last until their next pick at #61. At least one Kings staffer wanted to stick to their list, but in the end they gambled and they still got Simmonds. Simmonds said he was driving when his agent called him with the news. I think he said he had to pull over in order to process everything.
Pre-1992 the rules with the European players was a bit strange although it's easy to take for granted that drafting from USSR/Czechoslovakia was uncharted territory to some degree. There was a rule about a first time European draft eligible only being able to be drafted in the first three rounds unless he had a certain number of games (with the senior team?). This led to a lot of confusion with Vancouver taking Pavel Bure with a sixth rounder in 1989 when most of the league was under the impression that he had to go in the first three rounds or wait another year.
THN listed Kasparaitis as an honorable mention in its 1991 Draft Preview (somewhere ranked 45-70). Alexei Kovalev was also listed as an honorable mention and would be the first Soviet taken in the 1st round in 1991. USSR dissolved in December 1991 which would open things up. The Rangers taking Kovalev #15 was a bit of a surprise in 1991, but the following year Alexei Yashin went #2. So that might be an indicator of how things quickly changed.
Edit: draft day video of Kovalev
To that point teams weren't entirely sure when they could get those guys to sign. Veterans like Fetisov/Larionov had to endure a lot of red tape to come over later in their careers. Bure's status ended up going to court. Mogilny/Fedorov had to defect which was scandalous. Ditto guys like Petr Svoboda and Bobby Holik.
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Not sure if he ever submitted his draft paperwork in previous draft eligible years, but Ruslan Salei (RIP) went #9 in 1996 as a 21 year old. THN's Draft Preview says he fell through the cracks playing in Belarus. Salei played 1995-96 for Las Vegas of the IHL and played well.