Is anaerobic activity during ketosis possible?
You are correct in thinking that fatty acids cannot be metabolised anaerobically. However, in the type of metabolic state that you are describing, blood glucose will be maintained by the liver to support tissues or cells which are more or less dependent upon anaerobic metabolism. The classic example of such a cell type is the red blood cell which as no mitochondria and so cannot use the TCA cycle. The brain is also heavily dependent upon glucose.

The liver exports glucose that it has produced via gluconeogenesis from amino acid skeletons, as well as from glycerol produced as a result of fat metabolism.