I agree that castration, which medically means removal of the testes without penectomy (removal of the penis), under the conditions that existed during the time frame being discussed will result in some deaths due to uncontrolled bleeding or infection. The major issues do not have to do with instruments (the instruments of this period are not as different from modern instruments as you might think), or the surgical skill of the castrators who had significant experience. As noted the issues are uncontrolled bleeding and infection - at this time ligatures for vessels to control bleeding were not generally used, and of course use of antiseptics or sterilization was not used. While the relatively rich blood supply of this area could cause a problem with bleeding, these were smaller vessels which could be dealt with by direct pressure, a technique known and used at the time. This same blood supply mitigates against infection, although by no means eliminates it. It is worth noting that many surgical infections of the time, while causing suffering, would eventual end up healing - not all infections resulting in death by a long chalk.
Wars advanced trauma care from day one. Using that as an example, if we assume that castration becomes something being done not to prisoners or slaves who are, to some extent, disposable, but rather to "citizens" of value, you'll see efforts made to improve techniques. Again, remember that gelding of valuable livestock was widespread, and this skill can transfer. This doesn't mean you'll see some major overall advance in medicine, this requires a good deal of scientific advancement across the board. More widespread castration, both adult and childhood, of non-slaves/prisoners, on a voluntary basis for religious reasons, will result in better techniques and reduced mortality and morbidity.