Yes, of course. ;-)
Bunnies do not breed during the winter, but start breeding at spring. Thus, newborn bunnies appear at spring. Birds also do not breed during the winter, but in spring. Thus, to look for hidden eggs does not make sense during the winter, but makes sense during spring. Thus, to look for hidden eggs starts to make sense once one can see the first newborn bunnies.
Above things are likely to be known to children - once people see a newborn bunny, they are likely to tell this to nearby children too, and these children are likely to observe a correlation between seeing bunnies during springtime and starting search for hidden eggs in Nature. To mingle correlation with causation is a common error even among adults, so it is quite likely that children will develop similar explanations for the observed correlation.
Many adults like to make jokes with stupid children, so, once they observe such a funny theory, they can, with some probability, support it by hiding even more eggs to have more fun about that stupid kid which believes such nonsense. And, then, this can easily become a "running joke" which will be traditionally repeated every year.
So, I do not believe in the particular claim about the behaviour of Easter Bunnies. But, once I believe that young bunnies in nature will be visible with much higher probability during Easter time than during the winter, one can, with some simplification, say that I believe in the "Easter Bunny".