I am not 100% sure (I have not done this quest) but most likely the answer is "no" because the situation may be similar to The Gravedigger of Drefia Quest and Gravedigger mount which cannot be tamed without first completing the quest so here it can be similar and even if you have the whole object assembled, you won't be able to tame the griffin.
Question Revival V contestMarch 17, 2024
Interview with Solkrin - lead of the Customer Support team at CipSoftDecember 20, 2023
Become a TibiaQA Supporter!May 09, 2023