I've readed a little bit of Orpheus, and I'm running a Dark Ages Vampire chronicle, but I was wondering if it's possible that something like Orpheus could exist in Dark Ages (just for NPCs or something like that, not for players).
The answer is, of course, yes, to any question like "can it be done in RPG X" Sure, as long as you're willing to put in the work on the backstory. It is, after all, a (dark) fantasy game, meaning whatever you can imagine, you can work into a game that you want to run. RPG's exist to explore hypotheticals like this.
However, if you're asking what the real history of this is, and whether it would reasonably fit into the setting: A) I don't think so, not in its current form, and B) this ventures into History Stack Exchange territory.
Ghost hunters (which is, in essence what the Orpheus Group is) in the Dark Ages are going to have a completely different rationale than modern day ghost hunters. The idly curious are discouraged, and may be accused of trafficking with demons themselves. The only people with a legitimate claim to exploring the supernatural will be the church, and those will be monitored extensively.
If you don't go the clergy route, that leaves you with people who do not have a socially legitimate reason, and these will instantly be labeled heretics. Remember also that, in the Dark Ages, the common people are extremely superstitious, and would not only fear the supernatural, but also fear those who have an interest in the supernatural.
All of that said, you have unlimited artistic and creative license to do whatever you want in your campaign. You can run Dark Ages Scooby Doo if you want. It will, however, alter the default assumed setting of WoD Dark Ages. I'm not sure, from your question, whether altering the setting is really your concern or not.