As someone that works with low noise systems but on the firmware/software side, is it possible to design a low noise power supply with a switcher, without some kind of linear stage (like a final LDO regulator)? The hardware engineers are good, but I'd like to understand this a bit myself.
In principle yes, in practice it's rarely worth the cost and complexity.
If you're careful about the converter design (keep the high-current loops extremely short, use counter-rotating loops to tightly confine magnetic field within those short loops, use a soft-switching topology to reduce EMI and sharp edges at the switch node, switch quickly or use multiple parallel converters at different phase offsets to reduce magnitude of current ripple), you can get decently low noise. There's a good Jim Williams app note about this.[0]
But it's almost never worth it to do this, since there's LDOs with two or three orders of magnitude better noise voltage. There's a time and a place for a really low noise converter; usually EMI constrained galvanically isolated converters like medical supplies or scientific instruments need them and aren't too sensitive to the cost or development effort. But even then, you'll often find LDOs cascaded on the outputs just afterward, since a good LDO can add another two orders of magnitude of ripple rejection in the switching frequency band.
