Serious answer: apples & oranges here.
No, I don't think our system is so unique that it would take any player much longer to adjust to us than to adjust with another team. But a sizeable adjustment period is the NORM, not the exception, when you have a player going to a new team.
There are also pretty substantial differences between Rakell and Giroux.
Firstly, Giroux is a bonafide superstar. Sure, he's slowed down a bit since his prime, but Giroux is FOURTH behind only Crosby, Ovechkin and Patrick Kane in points in the NHL since 2010. He has elite, elite hockey sense. Comparing him to Rakell, just in terms of sheer ability and also experience is not a fair comparison. Giroux has always been a guy who drives play; Rakell has always been a complementary player, not a driver. He's averaged 50% more points per game than Rakell in his career.
Second, Giroux was traded on Saturday, and he has known for weeks it was Florida and nowhere else he wanted to go. There was no time difference or difficult travel. Giroux probably flew down on a private jet and he had several days before he was inserted into the lineup. He was traded Saturday, and his first game was Thursday.
Lastly, Giroux played his first game against the team with the worst record in the NHL. He got traded to the highest scoring team in the NHL, and played his first game against the last place team in the NHL. And while Jeff Carter is a nice player these days, Giroux was playing next to Alex Barkov, who is a top 5-7 center in the NHL and is putting up more ppg than Sidney Crosby. And Giroux's other assist came on the first unit of a Top 5 Power Play in the NHL, playing with 3 guys who are averaging over a point per game (Barkov, Huberdeau and Reinhart). So yeah, it's no surprise he picked up 2 secondary assists.
Rakell is not Giroux, Pittsburgh is not Florida, and Carter is not Barkov/Huberdeau. So I think it's fair to give Rakell more time to adjust and see how he does if he gets meaningful time with Crosby or Malkin, although unlike Giroux we know Rakell is not going to be on the first unit PP. This isn't about Sullivan.