I know I might sound crazy, but hear me out:

-We can't know the toucan's colors for sure because the shirt it appears on is 2-tone only, but we can guess that the light areas are light and the dark areas are dark on the real thing.
-Both have light fronts. Toucan's light color appears to go from around its eyes to its feet, while Pikipek's goes from its eyes to it's chest. Expanding colors in Pokemon is not uncommon as they evolve (sfor example, the white on Popplio-Brionne-Popplio3).
-Both have plain, dark colored outer wings.
-Both have a dark area on the end of their beak.
-In the real world, woodpeckers and toucans are (distantly) related. Both are classified under the order of Piciformes, though this does include other families such as jacamars, puffbirds, barbets, and honeyguides.
-Pikipek is said to drill into trees to store food, like real-life woodpeckers do. Toucans, while they apparently do not burrow into trees, apparently do use holes dug by other species, including woodpeckers, to nest/store food, too.
-Regional birds have (especially recently) altered species as they evolve. Pidove to Unfezant and Fletchling to Talonflame, for example.

I think, taken altogether, there is a decent possibility that they are related. Even if not directly by evolution, though that is what I think, at least as some sort of counter-part.