I don't know enough about Angel to know about what might have affected his ordination.

The last rites as such may only be performed by a priest; I don't know whether there's any reason a cyborg couldn't be a priest, though. Any baptised person can validly (but not necessarily licitly) administer baptism, but perhaps baptism is not the best idea if you have electronics in your head.

edit: you know, kadath is right, you don't have to be baptised to administer baptism and I am talking nonsense there. Sorry.