Absolutely not. Draining the old brake fluid from your brake before starting the bleed process would be making the job a whole lot harder.
As fluid leaves your brake system it is replaced with air and since the sole reason for bleeding your brakes is to remove all air from inside the brake system filling it with air beforehand is madness.
The old, discoloured brake fluid will be replaced with new during the bleed procedure. As new brake fluid enters the system it will force out the old, discoloured fluid.