I suppose that if you boosted the bass frequencies by 6dB and then did a system level check with pink noise, you might find that the overall level of the system has risen one or two dB.
What would this mean? You might find that, at the calibration volume level, the affected speakers are reading about 77dB instead of 75dB.
But more important than the absolute output level of each speaker is the relative volume of each speaker. If you have different types of speakers for differing positions in the room, and each responds differently to boosting a range of frequencies, then you will have affected the balance of the system.
More to consider: unless a system is perfect in every way (who has one of those?), there is a bit more to ponder (or worry) about. If you boost frequencies below 600Hz, for instance, and subsequently boost the output of you surround speakers a couple dB to match the fronts which might be more efficient in the low end than the surrounds, then when you have sounds which are in the 3000Hz range, the surrounds are now two dB higher than the fronts at these higher frequencies.
What to do?
First, realize that these types of inequities existed even before you used the tone controls. The point of the pink noise was to adjust for an equal average energy level over a wide range of frequencies. If the surrounds have a different frequency response curve (due to their construction and placement in the room) than the fronts, then, even if the average output for all frequencies matches the fronts, some narrow bands of frequencies may be more pronounced in the fronts, other narrow bands more pronounced in the surrounds, no matter how you adjust the average levels of each channel compared to the other. This means that adjusting the tone controls has not introduced a new problem, but perhaps just made you aware of one that existed all along.
Second, no system I know of is going to be perfect, so don’t sweat it much. The bottom line is always going to be, “does the performance of the system give me a level of satisfaction?” So, if your system is calibrated without adjusting the tone controls, go ahead and change the bass or treble a bit, then listen to bits of several favorite source materials and see if things still seem in balance or not. My guess would be that, unless you are adjusting the treble or bass radically, you are not going to have to worry about system calibration.
If you want to re-calibrate to see the difference, it won’t hurt. Just write down the adjusted dB numbers from the on-screen menu for each channel first, that way you can easily go back if you want to.