Does the word "saw" imply that the farmer found the duckling by "coincidence"?
No, the word "saw" by itself does not imply that the farmer found the duckling coincidentally. However, in this context, it can be assumed that he discovered the duckling by chance since he was out doing work on the farm early in the morning and he wasn't specifically searching for the duck. If you want to imply that he came across the duckling by chance, you can say "happened to see". Ex: They saw a celebrity walking across the street in Los Angeles. Ex: They happened to see a celebrity walking across the street in Los Angeles.
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