Would any copies have the ability to continue copying other creatures
Once your original {Essence of the Wild} dies, or is removed from the field, all your other creatures that entered the battlefield as a copy will still have its ability, power, toughness, etc.
In short yes, they are exact copies of it, so if the original dies, you still have a bunch of guys on the field with the same copy ability
And to be thorough, here's your ruling about the copiable characteristics of a card:
503.2. When copying an object, the copy acquires the copiable values of the original objects characteristics (name, mana cost, color, card type, supertype, subtype, expansion symbol, rules text, power, toughness, loyalty) and, for an object on the stack, choices made when playing it (mode, targets, the value of X, whether a kicker cost was paid, how it will affect multiple targets, and so on). The copiable values are the values that are printed on the object, as modified by other copy effects, by as . . . comes into play and as . . . is turned face up abilities that set characteristics, and by abilities that caused the object to be face down. Other effects (including type-changing and text-changing effects), status, and counters are not copied.