Unfortunately, no. When I was around 300 lv the Gryphon mount was a dream to me, so I searched extensively through all foruns and wikis about tibia, finding only one negative answer here at TibiaQA . I'll expand it by provinding all the answers to the questions I had but couldn't find.
At the time, not satisfied with the information I found, I did buy the item Regalia Of Suon aaaaand... no, it was not possible. Spoilers state that you have to wear the gryphon mask in order to tame it, but borrowing or buying it won't work either. When I tried, I even ran to the nest trying to obtain it by myself, but sadly you can't "find" it in the nest without the correct quest mission.
Even if you get to the mask part, you DO have to finish all Kilmaresh missions in order to tame the Gryphon. I guess this is part of the lore as when you tame it, it says that you have it's "permission". Going through all the challenges that The Kilmaresh Quest imposes proves that you are a worthy Gryphon rider, and it is a privilege for only a few.