We understand by cauterization of the uterine cervix, the healing of a pre-existing lesion in the uterus, which can be by resection or vaporization. Normally, we refer in these cases to warts (condylomatous or not) and to dysplastic lesions of the junction of the columnar epithelium and the polystratified epithelium in the ectocervix.
Once the disease is overcome, the cervix retains its normal anatomy and physiology, so that it poses no impediment to conception and delivery in spontaneous gestations.
In vitro fertilization (IVF) is the fertilization of the oocyte in the reproductive laboratory, so the cervix does not play a role in this process. Blastocyst transfer is always performed in the absence of cervical lesions, as this is tested by cytology and previous cultures.
Embryo transfer should not be performed in the presence of any cervical lesion until it has been fully studied and properly treated. A gestation with a cervical lesion would preclude proper treatment of the lesion in view of the danger of the cytotoxic drugs that would have to be used.
The answer is therefore that IVF after cervical cauterization is no more risky.