Well, no.
The eggs became associated with Easter because many people avoided eating them during Lent. The last eggs got used up on Mardi Gras (Pancake Tuesday), and being allowed to eat them again was part of the Easter festivities.
Seems we have conflicting sources
The pagan roots of Easter | Heather McDougall
"
All the fun things about Easter are pagan. Bunnies are a leftover from the pagan festival of
Eostre, a great northern goddess whose symbol was a rabbit or hare. Exchange of eggs is an ancient custom, celebrated by many cultures. Hot cross buns are very ancient too. In the Old Testament we see the Israelites baking sweet buns for an idol, and religious leaders trying to put a stop to it. The early church clergy also tried to put a stop to sacred cakes being baked at Easter. In the end, in the face of defiant cake-baking pagan women, they gave up and blessed the cake instead."
Origin of Easter: From pagan rituals to bunnies and chocolate eggs
"Well, it turns out
Easter actually began as a pagan festival celebrating spring in the Northern Hemisphere,
long before the advent of Christianity."
"But in English-speaking countries, and in Germany,
Easter takes its name from a pagan goddess from Anglo-Saxon England who was described in a book by the eighth-century English monk Bede.
"
Eostre was a
goddess of
spring or
renewal and that's why her feast is attached to the vernal equinox," Professor Cusack said.
"In Germany the festival is called Ostern, and the
goddess is called Ostara.""
"
Rabbits and eggs as ancient symbols of new life
Many of the pagan customs associated with the celebration of spring eventually became absorbed within Christianity as symbols of the resurrection of Jesus."
The Ancient Pagan Origins of Easter
"Most historians, including
Biblical scholars, agree that Easter was originally a pagan festival. According to the New Unger’s Bible Dictionary: “The word Easter is of Saxon origin,
Eastra, the goddess of spring, in whose honour sacrifices were offered about Passover time each year. By the eighth century Anglo–Saxons had adopted the name to designate the celebration of Christ’s resurrection.” However, even among those who maintain that Easter has pagan roots, there is some disagreement over which pagan tradition the festival emerged from."
"The most widely-practiced customs on Easter Sunday relate to the
symbol of the rabbit (‘Easter bunny’) and the egg. As outlined previously,
the rabbit was a symbol associated with Eostre, representing the beginning of
Springtime. Likewise, the egg has come to represent
Spring,
fertility and
renewal. In
Germanic mythology, it is said that
Ostara healed a wounded bird she found in the woods by
changing it into a hare. Still partially a bird, the hare showed its gratitude to the
goddess by laying eggs as gifts."