Can early symptoms of appendicitis be present for a week?

May be: Appendicitis usually develops quickly but inflammation associated with or precipitated by viral infection of lymphoid tissue or inflammatory disease of the intestine may be present for a few days prior to the appendicitis becoming manifest.

Not really: Appendicitis generally evolves over 12-24 hours. Either the diagnosis is made and the appendix is removed, or the appendix ruptures and other treatment ensues; the appendix may or may not be removed at a later date. Symptoms that persist for a week are unlikely to be related to appendicitis, but should still be evaluated. See your doctor.