It is likely not true.

Easter eggs come from pagan spring rituals in Eastern Europe among the Slavs (as well as other sources, I imagine; however, being Polish I know about the Slavic origin). Just as the article states, the egg was a sign of new life in the springtime.

When the Slavs converted to Christianity, the symbol of the egg was adapated to Christian theology. It now represented the new life we have in Christ and the empty shells after the hatching of chicks was seen as a sign of Christ’s empty tomb.

And that is why there are easter eggs (they are dyed to make them pretty).

The easter bunny has a similar origin. The goddess of spring was accompanied by a hare, a symbol of fertility. There was no theological significance to the hare come the advent of Christianity but it remained an easter tradition because little kids love bunnies.