No way, no how.

"Endorsement" is a perfectly useable word, and endorsation is just incorrectly verbing the noun.

You didn't find it in any dictionaries, and I hope you won't, 'cuz it's ugly.
And just because you found it used on this here internet thingy or elsewhere, doesn't mean it's correct.

(To confirm this latter point, I recently based a round of Hogwash [a definition-inventing game for rare words] on a misspelling in a book I was reading, resulting in my eating at least 31 varieties of crow).