Marie Ragghianti's case became the subject of a book, Marie, written by Peter Maas and published in 1983. The film rights were purchased by director Roger Donaldson, who, after traveling to Nashville to speak with the people involved with the original case, asked Thompson if he wanted to play himself. The resulting film, Marie, was Thompson's first acting role and was released in 1985. Roger Donaldson then cast Thompson in the part of CIA director in the 1987 film No Way Out. In 1990, he was cast as Ed Trudeau, the head of Dulles Airport, in the action sequel Die Hard 2, as Rear Admiral Painter in The Hunt for Red October, and as Big John, the President of NASCAR, in the movie Days of Thunder (patterned on Big Bill France). Thompson went on to appear in many films and television shows. A 1994 New York Times profile wrote, "When Hollywood directors need someone who can personify governmental power, they often turn to [Thompson]." He portrayed a fictional President of the United States in Last Best Chance, as well as two historical presidents: Ulysses S. Grant in Bury My Heart at Wounded Knee (2007) and the voice of Andrew Jackson in Rachel and Andrew Jackson: A Love Story (both produced for TV).  In the final months of his U.S. Senate term in 2002, Thompson joined the cast of the long-running NBC television series Law & Order, playing conservative District Attorney Arthur Branch for the next five years. Thompson began filming during the August 2002 Senate recess.  He made occasional appearances in the same role on other TV shows, such as Law & Order: Special Victims Unit, Law & Order: Criminal Intent, and the pilot episode of Conviction. On May 30, 2007, he asked to be released from the role, potentially in preparation for a presidential bid. Due to concerns about the equal-time rule, reruns featuring the Branch character were not shown on NBC while Thompson was a potential or actual presidential candidate, but TNT episodes were unaffected.  In May 2007, he took a break from acting to run for the Republican nomination for president in the 2008 election, winning 11 delegates before dropping out of the race in January 2008. In 2009, he returned to acting with a guest appearance on the ABC television series Life on Mars and in the movie Alleged, about the Scopes Trial.

Answer this question "Did Thompson immediately agree to play himself?" by extracting the answer from the text above.
The resulting film, Marie, was Thompson's first acting role and was released in 1985.