316 is a very corrosion-resistant stainless alloy, but also very tough to machine, even on full-size CNC equipment. It tends to work-harden if the cutter is rubbing rather than cutting, which means you must keep up a steady feedrate. I had a CNC Sherline mill for years but only machined the more common 304 stainless with it. Even there, shallow cuts to be able to maintain feedrate were necessary. You may be able to use a Nomad, but IMHO very small depth of cut (.002" maybe) with small cutters–.03" or so.
The Nomad is well accurate enough and the axis drives are up to the job. The limitation is the spindle torque, and that is to this point at least fixed by the spindle motor and electronics. I would be more comfortable machining stainless using my Tormach.
I put a couple of photos of a nickel-silver workpiece I machined over the weekend in the thread Nomad and Bronze? The Nomad machined the nickel silver very well. The machining time was about 3-1/2 hours. Do you really need 316L or would something like nickel silver be adequate for your jewelry?