No it will not. Like Sedrem said, your brake fluid level is low. When you corner hard, fluid will travel to one side of the container, resulting in an even lower level, and the warning light will go on.Anyway, tightening up the cables will probably solve both your problems.
You don't need to pull off the center console to get to the adjustment screws as it can be reached using an extension with a socket. They are not really adjustment screws per se as it will release tension and then once you tighten it back up and crank on the handle it will self adjust both cables equally.You should pull off the center console. 2 screws each side, unscrew the shift knob. The wires for the handbrake light are attached to the console, so you might have to pull one of the attachments off to get the console clear of the shift.
Then you will see the adjustment screws for the brake. Pretty straight forward.
Your calbes have stretched and might be quite old. The little boot at the brake end of the cables rot away, and water gets into the cables, and the bend in the cables holds the water. When cold weather hits, you can then be left with a stuck-on hand brake in the morning. I had to take the other car, and forgot to leave the car in gear, and when the temperature warmed up enough, it came within inches of hitting another car.
Anyway, tightening up the cables will probably solve both your problems.