No. As Goombah pointed out, the novel provides more detail. Here's the relevant passage (p.49 of the first edition paperback):

"It had been a busy but satisfying day [Connie's wedding day] for Tom Hagen. Genco Abbandando had died at 3 in the morning, and when Don Corleone returned from the hospital, he had informed Hagen that he was officially the new consigliere to the family."