Can I use dispensers or droppers to auto-replant crops?
In vanilla Minecraft, wheat, carrots, and potatoes must be planted by hand, although they can be automatically harvested with water or pistons.
You might be able to get the functionality you want with a mod, but I don't know of any. Sorry!
No, dispenser nor droppers can plant seeds. However, as an alternative you can put a villager farmer there and he will automatically plant seeds.