How fast can treatment make a sarcoma go away, if the CT scan turns out to be sarcoma?

Depends. Sarcoma is a cancer of the soft tissues, usually muscle, bone, and/or fat. Treatment will vary on each individual patient with consideration for tumor size/location and cell type. It can involve surgery followed by chemotherapy or chemotherapy alone.
Hours to lifetime. Most sarcomas require surgery, so the few hours it takes to do the surgery will make the sarcoma go away. Some require chemotherapy and/or radiation. Chemo usually takes 6 months to a year; radiation about 6 weeks. There is always risk of recurrence or metastasis, so long term follow up is mandatory. More treatment may be needed if sarcoma recurs or spreads.