In theory it is possible to carburize any steel as long as the carbon concentration of the atmosphere is higher than that of the surface. In practice, yes this steel can be carburized using a typical setup. As a reference point, the European standard EN 10084 Case hardening steels – Technical delivery conditions lists 28Cr4 (1.7030) as a standard grade with a carbon content range of 0,24 to 0,31. Obviously most grades are in the range of 0.17-0.24, but there are exceptions.
I wouldn't want to. The high silicon content is likely to give you problems. I'd also expect the core hardenss to be rather high unless you are dealing with a large section. I'd also expect the toughness of the core to be lower than you'd get with, say, a 4815/4820 material. It really wouldn't be my choice of material for most carburizing applications.