Measurements using spectrum analyzer
The phase noise of the spectrum analyser is -100 dBc worst case, -110 dBc typical. This is (hopefully) worse than the synthesiser you are trying to measure. So no, you won't have much luck seeing your synth phase noise above that of the S/A local oscillator. This is not unusual. Spectrum analysers often have worse phase noise than synthesisers. I haven't needed to do this test for a while so I'm not up to date with the test equipment available. One technique I have used is to phase-lock a low phase noise signal generator to the synth output. A ring mixer is used as a phase comparator, which results in the signal generator and synth being in quadrature. The phase noise sidebands then appear at the mixer output at baseband. That is, phase noise at 100 kHz offset appears at 100 kHz at the mixer output, both sidebands superimposed. Your signal generator needs to have FM modulation capability down to DC in order to lock. You may also be able to infer phase noise performance in your final system by measuring reciprocal mixing performance.
You may have trouble seeing -106 dBc ref spurs in the noise.