i guess it depends how you are defining a learning disability? if someone is just below average well no... if someone has a boarderline intellectual disability then i believe they are likely eligible
the special Olympics is for those who have a cognitive disability (they can also have a physical one but they must have a cognitive disability) the paraolympics are for those with a physical disability
well i don't know about there but here in Australia you have to be identified by a medical professional as having an intellectual disability, cognitive delay, or closely related developmental disability