Can't work that way.
Say we have a zoo with 8 elephants.
Then the bombs drop.
Well, unless the zoo keepers unlocked the cages then they're gonna starve to death.
So let's say that some bombing happened at this zoo and let the creatures out, this would mean that at least 3 elephants would have to have died.
Then when they finally get out, 8 of them, how are they going to be able to reproduce sufficiently enough to survive for generations?
Or even survive the nuclear wasteland?
How are they going to survive the mutants that the wastes bring?
A zoo is not the solution for this, hell, cats were widespread before the Great War and they all became extinct because humans ate them.
Who's to say "any" animal from a zoo would have a better chance at survival.
It simply doesn't make any sense to me, logically, how any animals from a zoo is going to survive the wastes.