Is it possible to get the badges in the same order as Ash?

[Petzbreeder]

I have never completed Red/Blue/Yellow/Fire Red/Leaf Green before. I noticed that Ash gets his badges in the anime in a different order than we do in the games.

Ash got his badges in this order:
Boulder Badge (Brock)
Cascade Badge (Misty)
Thunder Badge (Lt. Surge)
Marsh Badge (Sabrina)
Rainbow Badge (Erika)
Soul Badge (Koga)
Volcano Badge (Blaine)
Earth Badge (Team Rocket)

We get our badges in this order:
Boulder Badge (Brock)
Cascade Badge (Misty)
Thunder Badge (Lt. Surge)
Rainbow Badge (Erika)
Soul Badge (Koga)
Marsh Badge (Sabrina)
Volcano Badge (Blaine)
Earth Badge (Giovanni)

Is it possible to get the badges in the same order as Ash did in the anime?

[Del]

Yes, I'm pretty sure gyms 4, 5 and 6 can be obtained in almost any order since the game is fairly open at that point. You could probably even get Blaine and Giovanni's before some of the others. But bare in mind that Sabrina's gym is a lot tougher than Erika's so it'd likely be a struggle.

This TAS speedrun video demonstrates the player obtaining Blaine's badge before collecting Erika's, for example.

[Petzbreeder]

You could probably even get Blaine and Giovanni's before some of the others.

Since Surf is required to get to Blaine, getting the Soul Badge is effectively a requirement. I'll definitely try to mix the order around a bit to make playing more interesting.

[Captain Jigglypuff]

I usually get the Soul Badge before the Marsh Badge.