You can go there after beating the Elite Four.
Source: Personal experience.
I must admit though, having it so close in DriftVeil City made me feel bad about it being barred :/
In Black 2 and White 2, this location is inaccessible before entering the Hall of Fame, since the entrance from Route 7 is blocked by Marshal and the Tubeline Bridge entrance is blocked for weight testing. After entering the Hall of Fame, in addition to these two entrances becoming accessible, Clay completes his tunnel from Driftveil City into Twist Mountain, called the Clay Tunnel.
Confirmed by Bulbapedia.