I'm the world record holder (Cruel brawl) and yes I did manage to get 3222 Kills with pikachu in 1 run. Took me 6 days+.
Yes I am a stadium veteran. No I didn't use homebrew or hacks or any kind of cheating stuff.
But I'm not bragging with my scores at all though just wanted to let you know it's possible.
Oh and also, Pikachu could easily get into the 6000+ or even much higher. It all depends on the player and his patience. (Luck is also important but if you watch what you are doing thing's will go the way they should be.)
Link 1:
http://www.cyberscore.me.uk/chart-39230.php
Link 2:
http://allisbrawl.com/video/video.aspx?id=10023
Also, current World Record list:
258 - Mario ---------------------- GoV
174 - Donkey Kong ---------------- Zimer
84 - Link ----------------------- GoV
122 - Samus ---------------------- GoV
146 - Kirby ---------------------- Zimer
120 - Fox ------------------------ GoV
3222 - Pikachu -------------------- GoV
2337 - Marth ---------------------- GoV
176 - Mr. Game and Watch --------- GoV
76 - Luigi ---------------------- GoV
143 - Diddy ---------------------- GoV
123 - Zelda/Sheik ---------------- kavaz
383 - Pit ------------------------ Zimer
246 - Metaknight ----------------- GoV
169 - Falco ---------------------- Bill
148 - Pokemon Trainer------------- Zimer
98 - Ike ------------------------ GoV
131 - Snake ---------------------- GoV
159 - Peach ---------------------- Zimer GoV
75 - Yoshi ---------------------- Zimer
73 - Ganondorf ------------------ GoV
62 - Ice Climbers --------------- GoV
61 - King Dedede ---------------- GoV
81 - Wolf ----------------------- GoV
166 - Lucario -------------------- GoV
77 - Ness ----------------------- Zimer
63 - Sonic ---------------------- GoV
147 - Bowser --------------------- GoV
63 - Wario ---------------------- GoV
223 - Toon Link ------------------ GoV
498 - R.O.B. --------------------- GoV
84 - Olimar --------------------- GoV
77 - Captain Falcon ------------- GoV
143 - Jigglypuff ----------------- Zimer
83 - Lucas ---------------------- GoV
10010 - Total --------------------- GoV
Enjoy.