Frankly, I'm skeptical about the claim that Pikachu takes control of Groudon, as well as the claim that it has Groudon's abilities. Groudon's tier is slightly LESS of a maybe.
The episodes where this occurs:
https://bulbapedia.bulbagarden.net/wiki/AG097
https://bulbapedia.bulbagarden.net/wiki/AG098
I recall watching them a while back, & although my memory on dialogue & such is foggy, the episode summaries are fairly detailed. I'm a bit lazy to hunt down the episode footage myself for better reference.
Looking into it, it seems that the Blue Orb (Groudon's Orb) goes into Pikachu's body. Similarly, the Red Orb (Kyogre's Orb) later goes into Archie's body. I don't recall the scene of Archie absorbing the Red Orb, but here's how Bulbapedia describes it....
"Suddenly, the Red Orb he's holding absorbs into his hand, in the same way the Blue Orb did with Pikachu. Archie screams, then laughs insanely as the orb's throbbing markings appear on his chest."
Notably, possessed Archie is able to sic Kyogre on Brock & May after they have Beautifly & Mudkip unbalance his helicopter. It also listens to him & reacts (with an ineffectual giant wave) when Archie warns it of an incoming Solar Beam.
Bulbapedia says this about Pikachu absorbing the Blue Orb:
"Suddenly, a quick cutscene shows an opening eye and a growl, and the Blue Orb starts to glow and absorb itself into Pikachu's body. Pikachu writhes in pain briefly, and at Maxie's suggestion, Tabitha takes the opportunity to have the Mightyena attack. Hearing them, a possessed Pikachu turns around and defeats all three with a supercharged Thunderbolt. Pikachu sways back and forth from the strain,"
Further into the episode's summary:
"Pikachu is still in pain from having absorbed the Blue Orb. Suddenly, he glows with those red markings again and breaks free of Ash's grip. He then basically goes insane, letting out massive bursts of electricity everywhere, including one that just misses Ash, before finally fainting from the strain."
"Still captive in Team Magma's helicopter, Ash is holding Pikachu, trying desperately to calm him down as he goes insane again, letting out bolts of electricity everywhere. Ash is getting hurt, but won't let go of Pikachu this time."
The next episode:
"Kyogre's disturbance causes a tremor that makes the downed Magma helicopter to shift, throwing Ash and Pikachu around. The same tremor throws Lance and Maxie to the ground. Inside, Pikachu awakens, and his body is taken over by the orb again. He goes insane again, and one of his attacks causes a small hole that's just big enough for him to leap through. He does so and runs off."
Later on, Pikachu channels lightning from the storm for a power up. One of the biggest lightning bolt hits Pikachu & Groudon's containment box, awakening Groudon. Then a volcano erupts as Groudon awakens. Pikachu soon after lands on Groudon's head, & later helps it by using a super-powered Thunderbolt to stop Kyogre's Hydro Pump that was aimed at Groudon.
Apparently, it's after Solar Beam lands a powerful hit on Kyogre that Archie's body begins rejecting the Red Orb. It emerges from his body, & he faints. The same thing then suddenly happens to Pikachu, who faints & falls off of Groudon's head.
Pikachu falls into the ocean, Ash jumps in after, Kyogre rescues both and....
"Max then points out the two orbs, rising in the air and circling each other. They combine into one, and then dissipate. Groudon and Kyogre stare at each other briefly, and now that neither of them is linked to an orb, they retreat back to their respective lairs: Groudon into the volcano, and Kyogre to an ocean trench. Lance and the others discuss the day's events, and Lance says that the two legendary Pokémo will start a new world, as Ash wonders where they'll go."
RIP Red and Blue orbs apparently. Also, Kyogre & Groudon creating a "new world"? Like a new community of Pokemon? May need to check dialogue for that.
So yeah. The Blue Orb caused Pikachu pain, strain, fatigue, made it go berserk, resist Ash, & deliberately awaken & help out Groudon. All the while, Pikachu ONLY used electricity abilities. Albeit, amped ones, even without channeling Kyogre's storms.
But the closest it came to USING Groudon's own abilities was using lightning to awaken an imprisoned Groudon and only THEN, after Groudon awoke, did Drought trigger.
Notably, in this form, Pikachu stopped one of Kyogre's Hydro Pumps with a Thunderbolt.
Pikachu definitely wasn't acting like itself, given it defied Ash & gladly ignored him. I'd dare say it was under Groudon's control. By contrast, Archie with the Red Orb in him controlled Kyogre, rather than the other way around. Human bias by the orbs?
And as mentioned above, when Kyogre took a big hit, the Red Orb exited Archie's body, he fainted, & for reasons I'm not clear on -if there are any- Pikachu lost its orb too, and also fainted. So, damage suffered by the Legendary also occurs for the Orb-affected, too?
Viewing the episodes might still help divulge some stuff. In any case, I hope this can help draw some conclusions.