No. Syphilis has pretty well defined stages, and after you get the initial chancre, it would then move on to other symptoms.
Periodic sores on your genitals sounds like herpes. Ask your doctor for a type specific IgG blood test, and also to test you for syphilis if you think you have it. Syphilis is definitely among the infections you do not want to leave untreated. It can cause a LOT of severe problems if you do.
Aj