The Elemental Adept feat allows spells of a single damage type to ignore any resistance to that damage type. Does this effect apply to immunity as well? For instance, if I cast Fireball on a Fire Elemental, would it deal damage?
No, it does exactly what it says it does.
Spells you cast ignore resistance to damage of the chosen type.
It says nothing about immunity, so it doesn't affect immunity in any way.
If your DM's feeling generous, you might be able to persuade them that it should allow you to treat immunity as resistance, but that's entirely their call, and the rules don't support it.