Is Mercenary a 4th faction in Dragonfire?

No. Mercenary is not a 4th faction. That's the classic mistake to avoid.

The game always has 3 factions (for example North / Central / South). Mercenary is only a way of being placed into one of those 3:

• You accept a random placement among the 3 existing camps
• You get a gold reward for that flexibility
• You do end up in a normal faction (North, Central or South), not in a separate camp

So don't reason "3 factions + Mercenary = 4 camps". The correct reading is: 3 factions, and Mercenary is just a random-placement-plus-gold button that sends you into one of them. Useful for the game (it fills weak camps) and for you (the gold), but it stays an assignment option, never an extra faction.