Let's look at the scenario you presented:
The Pacers trade Paul George to the Lakers this off-season. Magic and Pelinka immediately offer him a max contract extension for the next three years, which he signs; because George is entering his eighth year in the NBA, he can earn up to 30% of the cap each year. The salary cap for the 2017-18 season is $102MM; 30% of that is $30.6MM. Over the course of the next three years, George will make $91.8MM.
Let's look at my scenario:
The Pacers trade Paul George to the Lakers this off-season. Magic and Pelinka immediately offer him a max contract extension for the next three years, but George refuses to sign it. He chooses to play on his current deal for the 2017-18 season ($19.5MM) and exercise his player option for the 2018-19 season. In the 2018 off-season, George meets with teams from around the league and decides to sign a max contract with the one he thinks will give him the best chance to win a championship. The salary cap for the 2018-19 season is projected to be $103MM; 30% of that is $30.9MM. In this scenario, George will make $81.3MM over the next three years.
Therefore, Paul George will make $10.5MM more over the next three years if he decides to sign a max contract extension with the Lakers after they trade for him. By doing so, George forfeits the opportunity to meet with any potential teams in 2018 who may be in a much better position to contend for a championship. George will be locked up until 2020 when he will be 30 years old; if the Lakers don't come close to winning a title in that time, he will lose three years of his prime to them. That is a lot to give up for only $11.1MM more for the 2017-18 season and only $10.5MM more over the next three years.
So, yes, I don't think it's a forgone conclusion that Paul George will sign a max contract extension this summer if the Lakers trade for him. I think he will use the upcoming season to decide whether he wants to continue playing for the Lakers for years to come, or whether he wants to exercise his player option in 2018 and take his talents to a team that is better equipped to contend for a championship during his prime.