I agree. Even if you amplify the signal, the "signal" power in the given measurement bandwidth (spectrum analyzer BW) is only a very small fraction of the total noise power.
Let's assume you have a noise source followed by a nice power amplifier, with total output power of 1 Watt, over a 1 GHz bandwidth.
Now let's assume you want to measure a filter and use 10kHz spectrum analyzer bandwidth.
The noise "signal" in this 10kHz band is 1W * 10kHz/1GHz = 10µW
This low "signal" means that dynamic range of your measurement is bad.
And unlike measurement with a tracking generator, you can not improve the signal/noise ration because your "signal" will also decrease when you reduce the bandwidth.
In my opinion, this concept is inefficient and you will get very poor performance. It is much easier to use a spectrum analyzer with tracking oscillator, where the RF power of the source is exactly in the measurement bandwidth.