No, Ludo Bagman is not a Death Eater. However, he was almost sent to Azkaban prison for conceding sensitive information to the Death Eater Augustus Rookwood, which is where the rumour of Ludo Bagman being a Death Eater originated. Ludo was later brought in for a trial in front of the Wizengamot and was considered to be sent to Azkaban by Barty Crouch. However, all charges against Ludo were dropped after it was proved that the major reason for his betrayal was the promise of a job in the Ministry.