Yes. "Kahvi" in nominative case translates to "a coffee" or "a cup of coffee" because as a liquid substance it is supposed to be a mass noun, and hence would require partitive case unless there is an implied countable noun paired with it, such as "kuppi". That's why the partitive case "kahvia" is semantically more like "some coffee" or just "coffee" without any determiner.
Kahvi? Is entirely correct. Kahviko is not how to ask someone if they want a coffe