When the 2 are not connected together:
Connecting the bias negative volts to the suppressor reduces the sensitivity of the plate.
For one thing it will run a bit cooler like
To clear up this suppressor grid thing we first need to understand why the suppressor grid was added & also what happens inside the tube under heavy conduction.
Electrons travel toward the plate with very high velocity, enough velocity that some electrons bounce right off the plate. This is known as secondary emission, exactly what the suppressor grid was added to "suppress".
During heavy conduction, the (negatively charged) electrons accumulating on the plate cause it's high positive potential to be reduced somewhat, leaving the screen grid as having the highest positive potential within the tube.
Without a functional suppressor grid, electrons that bounce back off the plate as secondary emission are attracted by the high positive potential of the screen grid, screen current rises & the plate is not operating as efficiently as it can.
Now, to applying a negative voltage to the suppressor grid,,,.
Note that both times I mentioned it, I said that a negative voltage is often "derived" from the negative bias voltage. I did not say to connect the bias voltage directly to the suppressor grid, as some online tutorials say to do. This is too high of a negative voltage & will result in the suppressor grid acting as a second control grid, thus causing the effects AMS mentions above.
What is required is that the suppressor grid be negative with respect to the cathode, enough that it repells the "secondary emission" electrons bouncing off the plate "back" to the plate, without it being so negative that it acts as a second control grid.
A suppressor grid negative voltage that is say, 1/5th or 1/6th the control grid's negative voltage should be fine.
Compared to a pentode that has the suppressor grid tied to the cathode, this will result in reduced screen grid current & increased plate current, as stated in that "tube Bible", the Radiotron Designers Handbook. Cheers