No. Mastitis as most women know it (decreased milk output, swollen/tender breast, fever and aches) probably cannot go untreated or else a breast abscess may form. Very early "mastitis" that has slight symptoms such as mild firmness in an area of the breast, and a mild decrease in milk output, may resolve with breastfeeding, pumping, and massage to get the milk out of the affected area.
Yes. Most mild cases of mastitis will resolve with warm compresses; pain relievers; continued nursing and pumping on the affected side to help release clogged ducts; and tincture of time. However, if one is moderately or severely ill, or if things are not getting better over the course of 2 or more days, treatment with antibiotics may be necessary. See your doctor if have any questions.