Hello fellow Beedrill fan!
Beedrill have a 385 base stat total in Gen 3 (well, that’s bad).
Beedrill is obtainable very early in route 2 and Viridian Forest.
In Gen 3, Beedrill is the only Pokemon who have one of the strongest bug type move in-game, being Pin-Missile.
It doesn’t have a good STAB poison-type move, only having access to Poison Sting. There is a Sludge Bomb TM in FRLG, but its post-game. (Correct me if I'm wrong)
It can’t help with Sabrina cause of its poison typing.
In conclusion, although obtain very early and have access to pin-missile, Beedrill is still outclassed by other poison and bug type Pokemon. Namely; Nidoking and Weezing for poison type, and Scyther, Pinsir and Venomoth for bug type.
although I love Beedrill, unfortunately I can't recommend using Beedrill :(
but, you could always use it early-game!
Hope I helped!