”Yes” but think about this way in many speakers the midrange and tweeter are much more effective than the bass especially the tweeter .Are you saying that an amp may provide 100W of power, for example, but the xovers dissipate 20W due to internal losses, so the drivers receive 80W, hence the noise is less audible?
So in for example many two ways there is an Lpad ( series and parallel resistor ) to the tweeter to dampen it , say 6 dB or 10 dB compared to the bass driver that means noise is dampened in equal amounts . Similar for the midrange in some speakers.
But wait was not the tweeter more sensitive so sound level is the same ? The drawback comes in the active version where you attenuate before the amplifier,but the amplifiers true noise level will always reach the much more sensitive driver undampened .
And in the passive speaker the noise is also filtered to the bass driver by the xover . Makes it less audible, in actives there is full range noise to every driver .
In practice there may be variations having a series resistor to a tweeter even in an active speaker is doable as the power involved can be single digit watts for music and if it’s >100dB sensitive it works fine .
IMO you may want active speakers anyway because the many other advantages they have , but be aware of self noise when choosing them .
IME my the ones I have are quiet KEF LS60 , LSX and audiosmile .
Had fostex and Adam monitors with more hiss in the past.