What happens if someone has syphilis but does not have a sore and has sex with someone, can that someone get the infection?

Maybe: The lesions of secondary syphilis are very infectious and tertiary syphilis can also be transmitted though not so efficiently.

Syphilis: There are three stages of syphilis. The primary stage usually involves a non-tender sore. This sore can be in the vagina, rectum, mouth or on any part of the skin that is exposed. The secondary stage, after the sore has healed, is usually seen as a odd rash on the feet and palms of the infected person. And, then the deadly stage is the brain or neurosyphilis. Syphilis is highly contagious.