I'm thinking about creatures immune to necrotic damage, for example, and Chill Touch's effect (on a hit, prevents gaining hit points). RAW, I'm leaning towards no, but wanted to confirm.
[RPG] Is a creature immune to a spell’s damage type immune to the spell’s other effects
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Immunity to a damage type does not, generally, confer immunity beyond that damage.
In the example of Chill Touch there are three effects: damage, preventing HP gain, and clinging. A resistance to necrotic damage does not prevent either of the other two effects; the second and third are each predicated on the hit, not upon the damage.
Compare this with the wording of a spell like Banishing Smite: "if this attack reduces the target...." If a target were immune to that (force) damage the banishment would not happen, as that banishment is predicated on (the effect of) the damage.