Well, though I'm honestly happy and relieved that someone has expressed interest in playing a Paleblood Hunter, there are two main points that might be problematic with the scenario you're considering here, [@Habibi359]. The first problem would be whether it would even be feasibly possible to become a false Paleblood Hunter while also qualifying as a Fire Dancer. Hmm...
[HIDER=Theorizing...]The problem is that the Fire Dancers were supposed to be a gang made up by Hunters, and not only haven't the church tried using false Paleblood on existing Hunters (and have in fact only just begun their first trial run with human subjects), I also sincerely doubt that such a thing would even work. The very reason people with Paleblood come to Yharnam is to be [I]cured[/I] of Paleblood, and indeed becoming a Hunter in all observed cases seems to cure the disease, leaving only whatever other alterations the Paleblood made to the Hunter before being purged. Hunters are immensely resilient and barely affected even by otherwise fatal maladies, as seen with Ashen Blood, the plague that most likely resulted in the eventual loss of the entirety of Old Yharnam, but which only weakens a Hunter's regenerative abilities for a matter of [I]seconds[/I] before being naturally purged. As a matter of fact, in the entirety of Bloodborne, the [I]only[/I] thing the Hunter-blood couldn't cure was the degenerative condition afflicting Gascoigne. It stands to reason, then, that a Hunter would most likely purge false Paleblood immediately after contracting it, and it is anybody's guess - including the Healing Church - whether it would remain in their system for long enough to qualify as false Paleblood Hunters.

One way to solve this could be to expand the membership pool of the Fire Dancers to include Yharnamites in addition to Hunters. Yharnamites are proven to be lesser than Hunters in a lot of ways in the game and lore, most importantly in this context in that they are not as resilient. It is theorized that Ashen Blood was spread by the Healing Church during its early days as a means to incentivize the inhabitants to receive blood ministration, since the antidote alone was not enough to cure it, and Yharnamites have generally received blood ministration in order to be healed or cured of [I]something[/I], so Yharnamites are probably more resistant to illness than normal humans. They are, however, provably more susceptible than Hunters. The beast patients that can be found throughout Old Yharnam, which were all almost certainly Yharnamites before becoming so, remain afflicted with Ashen Blood even long after receiving blood ministration. More interesting yet is the fact that Gilbert - the very first NPC encountered by the player in the game - is ill and grows progressively worse over the course of the game, until he is eventually claimed by the scourge of beasts and breaks out of his house to be slain by the player. This tells us that Gilbert was definitely a Yharnamite (he turned into a beast and immediately recognizes the player as a Hunter), but that he also suffers from something beyond normal blood ministration (he makes reference that "what inflicted [him] was incurable"). We further never hear about Paleblood Yharnamites - the only ones to reference the Hunter's Dream are other Hunters - so it is probably not a stretch that the blood ministration applied to Yharnamites is insufficient to cure Paleblood.

Finally, the game never makes reference that it is possible for a Yharnamite to become a Hunter - to have the treatment going from human to Yharnamite overwritten by treatment to become a Hunter - but it doesn't state that it's impossible either. So one might assume that it would be possible to inflict a Yharnamite with false Paleblood and then give them treatment to turn them into a Hunter, resulting in a false Paleblood Hunter.
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Short version: it might be possible if the character was a Yharnamite before, not a Hunter.

The other problem is simple: why in the world would the Healing Church risk an experiment that might turn a known enemy of the church into a practically immortal super-soldier? I'm not entirely sure how to explain my way out of that one... The character would have to have made a pretty convincing gesture to justify the church to want to risk turning them into a false Paleblood Hunter.