Probably not -- on the AC side, it can take care of diode recovery noise. Not that it's much. The diodes will also act as PIN diodes, gating the RF only when conducting; some still gets through (they have fairly high capacitance, say >100s pF), and most still gets through during the conduction peaks anyway ("most", given the peak-detecting nature of the analyzer), but it might still save a few dB, like spread spectrum does. (And finally, the parametric mixing with line frequency may split peaks itself, saving another dB or two even without SS.)
Plus, the filter should be as close to the outside world as possible, so the length of wire exposed to internal fields can be as short as possible. Having the rectifier and AC line components (fuse, switch, precharge if applicable) exposed makes the design more difficult.
Now, the DC output may also benefit from common mode stuff. I have a project in mind that's probably going to be easier to build with a DC link board followed by an inverter board, and keeping stray fields down inside the enclosure is most likely going to require (or at least benefit from) a common mode choke on that cable between. On the plus side, the boards can be RF-grounded to the enclosure, so the requirements are more like, a ferrite bead to add some impedance (reducing ground currents), rather than sheer attenuation to keep noise off an indefinite AC line run. But, it's still important, as it helps avoid noise induced in signal level cables and circuits, which means fewer things to isolate (ugh!). Plus, I kind of just want to see how quiet I can make something (advantages of personal projects!).
Tim