Embryo transfer is not painful. It requires the instertion of a very small catheter through the cervix and into the uterus. The embryos are then pushed through the catheter into the uterus. There is very little to no pain involved.
It would seem that the answer varies from situation to situation, person to person. Some people report pain, others report no pain. One woman reported pain felit in her first IVF, but not on her second.