Having only up to the Cascade badge, I should be blocked from going into Saffron City by the two guards at the gate. However, if I am outside the north-side of it, and keep trying to run south past them, I eventually get through. Sometimes I get a little farther through the gate than others (possibly it takes a while for the guards load), but with perseverance, I can get through to Saffron.
When I leave back through the gate to go north again, the guards stop yelling at me.
If I log out after this, I have difficultly logging back in. Restarting the game entirely, when I do get back on, I get kicked back to the Pokémon center in Cerulean.
Proof of Saffron, two badges:
I discovered this because the first time I went through the gate this happened, and the game goofed out on me. Trying again, I realized I wasn't supposed to. So the perseverance could be translated to random luck at some point.