What will happen is you will alter the bias point of the 6SN7 slightly, not enough to really matter. You will get a slightly flatter load line which means perhaps a
slight improvement in second harmonic distortion.
With the measurements you sent, a 140V B+ with a 33K load on the 6SN7, the load line will look like this. 1K cathode resistor with 2mA plate current and 2V on the cathode (Ohm's law again, R = V/I = 2V / 0.002A = 1K resistor). Approximate bias point is the green dot.
So, the 6SN7 voltage will be able to swing up to the B+ voltage (140V) and down until the grid hits close to 0V where it will start to draw current (roughly 40V) at a quiescent bias point of 70V. What that means is the peak-to-peak voltage swing across the load line will be limited by the negative voltage swing - it can swing up from 70 to 140 (+70V) but can only swing down from 70 to 40 (-30V), so it will clip if driven more than 60V peak-to-peak (30+30V).
So what does 60V peak-to-peak get you in terms of power? Into a 300Ohm load, and assuming unity gain from the cathode follower output tube (which will be slightly less than 1 in reality). I'll skip the math, but it is around 1.5W.
At anything near 1.5W, your ears will be damaged, so the main point is changing the bias won't matter as it will not effect the degree of unclipped power available to your headphones in any noticeable way, unless you are listening at > 1.5W, which will make you deaf in short order