Possibly. This depends on the degree of discomfort you are having and the type of work you do. Headaches can interfere with thinking and concentrating. You should not work if it puts you or your colleagues at risk or if you cannot be effective. This is an individual decision.
Unpredictable. This is the big challenge with this disease. Between headaches within a cluster (about 6-8 weeks), you will likely be sleep deprived, anxious (fearful of another headache coming) and generally frazzled, making work pretty tough. If you can handle these issues, then work. The severity of pain makes it impossible to continue doing anything - or doing any other activity - until the headache ends.