This answer contains spoilers for the Death House, and is based on my personal experience playing it as well as the Curse of Strahd source itself.
First things first, a "dedicated healer" is something that is seldom actually seen or used in DnD 5e. The game lends poor support to characters intending to use most of their time healing other characters, and healing output from spells is generally paltry compared to the amount of damage per turn. The best way to keep your friends alive is, in most cases, to help defeat their enemies quickly instead of trying to repair the damage they do on the fly.
That said, healing magic or other powers like the Healer feat are very useful for rescuing characters from zero hit points --- even a single hit point is enough to give them full actions next turn and prevent them from having to make death saves.
But Death House is not quite your average adventure. Yet another reminder: spoilers ahoy.
The Death House is extremely deadly, assuming your players make the wrong --- yet completely sensible --- choices. Combat encounters, usually being the most dangerous part, are actually not the worst thing here: rooms filled with poisonous fog and doors turned into spinning scythe blades will very quickly wear a party to the end of their resources, unless they are exceedingly lucky with their rolls. Loss of health is not easily avoidable even with conservative gameplay, and rescuing unconscious characters quickly becomes a liability without fast healing in the conditions of the house.
To illustrate: our party went in with full resources. We had a Paladin for healing, and my Monk had the Healer feat and a Healer's kit with me. We emerged with all slots expended, the entire Healer's kit used up, with two characters at zero HP, the other two at a single HP, and this was with me and the Paladin squeezing everything we could out of our respective healing resources in a manner many would consider cheesing. Death House is that deadly.
Suggestions to alleviate the deadliness
The house is not at all that dangerous if your players pick the right choices. Since I've warned you already about spoilers, I'll state it up front: to avoid the house turning against the PCs, a creature has to die at the sanctum in the basement. Being open about the deadliness of the adventure can prime your players to make the right choice there and accept the consequence of losing one of their own. While not obvious, the sacrifice does not have to be humanoid in nature: any creature will do. If you're feeling particularly merciful, give them a henchman NPC to tag along to sacrifice, after which the party can leave the house unhindered, or some animal they can capture for that purpose.
For a less merciful alternative, you can fudge the rules of the house slightly. My Curse of Strahd GM suggested that the house should be appeased when a PC dies, even not in the sanctum. This will preserve the feeling of deadliness, but politely spares your players of the unsavory decision on who to sacrifice and gives them a shot at leaving everyone alive. You can of course also extend the players' capabilities to some extent by giving them health potions, but this is a bit fickle alternative: it might happen that the PC carrying the potions turns into a single-point-of-failure whose unconsciousness dooms the whole party.
Overall, whether or not this kind and extent of deadliness is desirable is up to you and your party. The best you can do is warn them in advance, really, that this is not going to be their average heroic romp but rather a nightmarish situation their characters will be lucky to survive and that some PC deaths are the expected outcome. If you or your players want that heroic romp instead, I suggest not playing Death House with them.