Technically no... since both Gary Stu and Mary Sue is used for fanfiction characters, more specifically self insert characters; Who, is a person generally loved by all canon characters (for no reason). One can do anything well, and always wins. A character who doesn't have flaws and doesn't need any character growth.
Ash himself is an inherently flawed character... He's strong yes, but does he always win? no to a point where most fans just want to see him win a league. He's more mature for his age, because of the adventures his been through (The Ash that started his Kanto journey has grown to be a the mature and capable trainer that won 2nd place in the Kalos League). Still despite his growth - he's often emotional , hot headed and always looking for a Pokemon battle. But mature enough to take his loses with grace, showing a huge amount of empathy to both friends, pokemon, rivals, and enemies. That makes him have a certain affinity to gather people and Pokemon around him.
Also, a good writer can write a character with the 'Gary Stu' traits without it being a problem. Just look at Saitama, Madoka, and Koro Sensei from anime or Aragorn, Jon Snow, and Harry Potter in fiction. All of these characters have established and overpowering traits, getting allies from almost out of no where, yet they go through thought challenges.
If there is a clear Gary Stu in the series it's Tobias. A 'mysterious' character who appeared out of no where. Who's amazing in battle, dominating Ash with two Pokemon, and has the respect of two legendary Pokemon who then joins his team. heck he even won he's final match with only his Darkrai...
So in my opinion is Ash a Gary Stu...
No.