Is Nick Carroway in any way implicated in the unfolding drama in The Great Gatsby?
Your question is a little ambiguous. If by "drama" you mean the vehicular murder of Myrtle Wilson, then it is hard to see how Nick could be implicated. To implicate is to show a person has some moral and legal responsibility in a harmful event or action. The main reason Nick cannot be implicated in Myrtle's death is that he only meets her the day of the accident. Moreover, in the preceding fight at Myrtle's New York apartment, Nick is an uncomfortable witness rather than a participant.
(Nick) I wanted to get out and walk eastward toward the park through the soft twilight but each time I tried to go I became entangled in some wild strident argument which pulled me back, as if with ropes, into my chair.
Yet, if Gatsby himself had not been at the apartment, Tom would not have behaved as he did and would not have challenged Gatsby in the way he did. It was Tom's aggressive behavior and his contempt for Gatsby, whom he feels he has tamed, neutralized and humiliated, that resulted in the ill will bred designations of who would ride with whom in which car. Seen from this perspective, it may be plausible to assign some implication of responsibility to Nick. This is because Nick facilitated the reunion between Gatsby and Daisy: if the reunion had not occurred, the entire situation would also not have occurred.
Furthermore, if by "drama" you mean Gatsby's death, the same logic would apply. Nick still is not implicated because he was acting out of friendship without any knowledge of the deeper tide of relationships involving the Wilsons and the Buchanans and Gatsby. Similarly though, it may be plausible to assign indirect implication of responsibility because, again, it was he who facilitated the reunion.