The octave/register key is not strictly required in order to play the notes in the second octave/register of a woodwind instrument, it merely makes them dramatically easier. The tiny hole it opens prevents the first harmonic from forming, causing the second (or third in the case of clarinet) to be the lowest frequency the tube can resonate. On saxophone, playing higher harmonics without the octave key is a basic exercise towards learning altissimo.
The octave/register vent will act as a tone hole as well, however. It's made as small as possible in order to minimize this, but the effect is an inevitability of physics. In fact, the standard Bb fingering of A key + register key uses the register vent for exactly that purpose. On a note like long B, the register vent causes the pitch to shade upwards slightly, which is what you're observing.