Yes, depending on the atomic structure stainless steel can be magnetic. The so-called martensitic and ferritic chrome steel are magnetisable, austenitic stainless steel is generally not magnetisable.
To guarantee formability with high temperatures, nickel and manganese will be added to industrial stainless steel. This is the reason why industrial stainless steel is often magnetisable. The load carrying capacity of bearings made of stainless steel is lower than the load carrying capacity of bearings made of chrome steel. Compared to austenitic steel, which isn't magnetisable, martensitic steel can be hardened. Thus a higher load carrying capacity can be achieved, which matters at many applications where bearings are used.
Magnetism isn't in correlation to corrosion resistance. You will find further information regarding corrosion resistance here.