No, none of this is true at all. What's Opera Doc was released in 1957, Bryan didn't die for another two years, and the (actual) last cartoon where he was the voice of Elmer was 1960's Person to Bunny. After Bryan died Elmer was voiced in three cartoons by a different actor, not by Blanc, and a fourth was released in which he had no lines, before the character was retired for the theatrical era.
And secondly the only line that Mel Blanc did as Elmer in this cartoon was when he shouts "SMOG!", and that was only because it was part of the joke. The only other time Blanc voiced Elmer during Bryan's lifetime was in The Scarlet Pumpernickle, where the producers decided it wasn't cost effective to bring in Bryan to record Elmer's minimal lines in the short. Also Elmer is voiced by a person named Dave Barry in the(pretty terrible) 1958 cartoon Pre-Hysterical Hare, as Bryan was part of a strike and reportedly refused to cross the picket lines.