The majority of you in this thread are already members of SDA, but I'll post the results of my test segmented run with the in-game trade Abra in Oreburgh.
Trade can be made prior to first gym (battle style switch until evolution), or you can fight the gym with the Machop first. For TAS purposes, I'm wondering if a Guts sweep would be best... Fight the two optional trainers in the gym, and the guy with rock type only in the mine while you're down there.
The Abra itself has a Quiet nature, but this only matters in two fights the entire game, both against the rival: Once against his Buizel (tied speed), and once against Floatzel
The IVs are as follows:
HP: 15
Attack: 15
Defense: 15
Special Attack: 25
Special Defense: 25
Speed: 20
You can obviously make use of teleport a bit before obtaining Fly.
Kadabra is able to OHKO nearly everything early-game, exceptions being there was one pokemon (I do forget which) which needed a critical Confusion (pre-Psybeam), and then there was a stunky (which happened right after I learned Miracle Eye, so not a major issue).
There was a Bronzor before shadow ball that needed a critical hit to OHKO, and the rest are contained in either the Commander Double battle with your ally, or in the Elite 4.
Control is established after beating the second gym for a little while. However, control is lost again right after obtaining lucky egg on route 209, and not regained until beating Crasher Wake at level 34, or 37, I forgot.
Control is then lost once more for part of the Byron battle.
The moveset I used was Grass Knot/Psychic/Shock Wave/Shadow Ball for most of the game. Shock Wave was especially useful in the fog. During the Elite 4, Shock Wave was replaced with Charge Beam for the OHKO + boosted special attack factor in lieu of X-specials. PP was really not an issue much at all: I only used a leppa berry, an ether, and an elixer, IIRC.
For the duration of the entire run, only one X item was needed (Commander fight with allied rival), and zero Rare Candies used. I also fought only the required fights, with the exception of the very first double battle in the game with the Grunts (before I discovered being able to skip them)
The "rival" fight right before challenging the Elite 4 was fairly easy. Charge Beam OHKO + special up against two of his Pokemon (he leads them in the right order too, which is great) and then Psychic will OHKO Snorlax.
Going into the Elite 4 with a level 76 Kadabra. Aaron's Drapion was mildly annoying, needing two charge beam power ups and a critcal hit. The rest of them are just laughable. Cynthia's Spiritomb even was really easy: Critical shadow ball does the trick. The final result was a level 83 Kadabra at the end of the Champion fight.
Shadow Ball and Psychic offer very nice neutral coverage. Later in the game, you can get away with a few Grass Knot and Shock Wave neutral OHKOs too, but they are mostly there for SE OHKOs before Psychic is available. Then of course there was the fog too. I think there were only two fights in the fog? I forgot already. The Ponyta was OHKOed with Shock Wave, and I believe the other two pokemon I fought were Psychic OHKOs.
Late game, when Charge Beam became needed for OHKOs, I was able to get away with some neutral OHKOs that were otherwise impossible (Shadow Ball against Cynthia's Roserade comes to mind)
If I remember any more, I will list them here, but I think this is the full list of Pokemon that were more than OHKO (after evolving into Kadabra):
That very first one that I mentioned before learning Psybeam (I really don't remember what it was, but I distinctly remember there only being one)
Grunt's Stunky
Random Bronzor before learning Shadow Ball
Byron's Bronzor (Shock Wave/Shadow Ball or Critical SB)
Byron's Bastiodon (2HKO Grass Knot/Critical hit Grass Knot)
Commander Mars' Bronzor (atop Memorial Pillar or whatever it's called where you get Palkia/Dialga. This one can be OHKOed with variable damage)
Commander Jupiter's Bronzor (same as above, but this one has different/higher special defenses and cannot be OHKOed without a critical hit)
Commander Jupiter's Purugly (same as above)
Commander Mars' Skuntank (issues due to Psychic immunity)
Ally's Munchlax (same fight as above. All it does is screech, so if you KO it, his Infernape is actually capable of doing something useful)
Palkia/Dialga (not important, but I guess worth mentioning)
Victory Road Trainer's Blissey
Rival's Snorlax (two upped special attacks, available via OHKO charge beam, makes up for this and enables a OHKO Psychic)
Aaron's Drapion (this fucker is difficult...it might be worth it to switch in Palkia to take it down.)
Lucian's Girafarig (Two Charge Beams, with stat ups each time)
Lucian's Bronzong (Two Shadow Balls/ a critical SB, after the stat ups from above)
Cynthia's Spiritomb (Charge Beam with a stat-up to SB)
Cynthia's Garchomp (Problem eliminated with the Charge Beam from above)
Cynthia's Milotic (See above)
That's about all I have on the subject. If someone wants to help me get a good emulator and such, I could run a test TAS on it, or I can leave it to you guys. (you'll probably have better results if you do it yourselves, tbh)