Not true. Rowling herself said there was no relation to this snake and Nagini. Nagini is a species of Viper and the snake in the zoo is a Boa Constrictor.
"Harry Potter And The Deathly Hallows - Part 2" Premieres
(L-R) Tom Felton, Emma Watson, Daniel Radcliffe, Rupert Grint and Matthew Lewis attend the New York premiere of "Harry Potter And The Deathly Hallows: Part at Avery Fisher Hall, Lincoln Center on July 2011 in New York City.
Harry Potter, Hermione Granger & Ron Weasley see Professor Lupin become a werewolf (Moony): Harry Potter and the Prisoner of Azkaban