Yes. I find it depends on the time of the month as well. In general, I have extra padding and know my body is not starving and have felt fine with light cardio and weight lifting in a fasted state. In practice I find I cannot fast the week before my period and certainly cannot workout fasted then because I feel too weak and exhausted.

Just listen to your body. If you're getting weak / dizzy try electrolytes like broth, if it doesn't help maybe you need to just rest or get some protein. It'll be different for everyone.