If it's the Sieg C0 'Baby' lathe you mean, I bought one about 3 years ago when I needed the cheapest and most compact machine available for a tiny workshop in temporary accommodation.
The machine is practically a clone of the Emco Unimat 3 with a few significant differences – a fully-variable speed, 150W power as against 90 for the Unimat, an integral base and tray and a 3-jaw scroll chuck as standard equipment.
I'd had a Unimat 3 for 20 years too in earlier life, and it's fair to say the Sieg C0 isn't as nicely made, but that doesn't necessarily mean it's less capable. It has the same significant drawback for speed of setting and operation – the saddle is permanently engaged to the leadscrew, leading to time-consuming winding back and forth. Accessories such as the pivoting compound slide and the powered longitudinal feed aren't as unreasonably expensive as they were fro the Emco.
A keyed chuck would also save you time and frustration as compared to the issued tommybar 3-jaw. Concentricity of the issued chuck is probably about average; I can see the runout with good round bar even though I've not measured it.
I'm sure that it's possible to make the components you mention on the C0 – I still use mine for small items occasionally, especially when my Warco is set up for something else.
However, given the positive comments some have made about the quality of some of the mini-lathes about at the moment, I think if I could possibly afford the space and the price, I'd probably investigate those quite seriously before going for the C0.