Depends a lot and what type of acne you have. Sometimes exfoliating and a light scrub can be beneficial, but if you're not pulling off deadskin and are just irritating things then you're doing more harm than good IMO.
Make sure you shower after your workout, especially if you're getting sweaty. Tanning definitely can help, just be wary of letting your skin dry out too much. You can get acne friendly moisturizers if your skin is becoming too dry.