Talking causually - yes, it's fine.
As you can have a spoonful, it is also possible to have half a spoonful, or a half spoonful.
However, it is important to note that these are very imprecise measurements, and many people will not take you literally when you say that. Instead, it will generally imply that you can only eat a very small amount of the ice-cream.
This is similar to when somebody says they'll have "just a french fry", but may actually take two or three.
For more precise measurements such as recipes, the exact type of spoon should be used and sometimes with the modifier "heaped":
Tablespoon, tbsp. e.g. 1/2 tbsp is half a tablespoon
Teaspoon, tsp. e.g. 1/2 tsp is half a teaspoon
Heaped tablespoon. e.g. 1 heaped tbsp, which is a tablespoon holding so much there is a little heap on top (as opposed to it being measured flat, up to the rim).
As pointed out in comments, Heaped may also be referred to as Heaping or Rounded, depending on the author.