Could a single dose of 1g azithromycin and 500mg ciprofloxacin be enough to treat chlamydia and gonorrhea infection?

No. Current cdc recommendations for gonorrhea and chlmydia are a single dose of Ceftriaxone 250 mg (shot) and a single dose of Azithromycin 1g (by mouth). Instead of Azithromycin you could do Doxycycline 100 mg by mouth twice a day for 7 days. Treatment for pelvic inflammatory disease (more severe infection in females) cannot be done in a single dose.