I work in an abortion clinic..
ALMOST ALL abortion clinics DO use anesthesia, but SOME do not.
Planned parenthood tends to NOT use anesthesia a lot... They tend to have a large number of appointments..
MY clinic includes the cost of IV anesthesia for all women, but some choose to have it because they may be breastfeeding.
Most clinics that I know of offers sedation/anesthesia, Planned parenthood and a few others do not, but most do.