Well, that is a complex issue. The basic answer is no. Being protected by divine power (from whatever source) and having your prayers answered is not necessarily evidence of being Holy or Sacred, but then that depends on your definition of these terms.
The point, though, is that Paladins do not have to be aligned with any specific church and they are not described as being ordained (unlike the Cleric who is singled out as being 'usually' ordained).
Paladins do not need to be members of any specific religion or order within a religion. Being righteous is enough. Many Paladins may eventually become ordained, but that is a different matter.
It's a very complex issue because the idea of a Paladin is rooted in real world religion, which is a subject that cannot be discussed. In general terms, the Paladin has not made any vows to a deity. He follows a very strict code of conduct, but unless inducted into a religious order, he remains a member of the laity.
Paladins are 'perfect' members of the laity. They are not bound by Clerical or Monastic regulations, though they may choose to become so.