Yes of course. But let me tell you something: the First World, the Second World and the Third World are outdated terms. Right now there are two better ways to name the countries: the Seven Worlds Index and the countries by wealthy.
In the Seven World Index, Costa Rica falls in the category LDC (Less Developed Country), along with all Latin America, Africa and most of Asia.
In the countries by wealthy there are just two categories: Developed Countries (the former First World and some countries from the Second World) and the Under Developed Countries (divided in four subcategories: Newly Industrialized Nation, Developing Country, Less Developed Country not Developing, and Least Developed Country).
Costa Rica, as a Under Developed Country, is a Developing Country (in some years it can be a Newly Industrialized Nation and many years later a Developed Country). Some people think that it can be a NIC (Newly Industrialized Nation), but actually only Mexico and Brazil, along with 9 other countries in Africa and Asia are Newly Industrialized Nations.
Costa Rica is a Developing Country, of course part of the former Third World. As a developing country, Costa Rica has poverty levels higher than that of the NIC countries, less per capita income, etc.
Among Developing Countries, Costa Rica is one of the wealthiest (along with Panama, Argentina, Chile, Vietnam, etc). Costa Rica has literacy rates higher than some NICs (eg: Mexico and Brazil).
In Latin America all countries are Under developed:
1.-NICs: Mexico, Brazil
2.-Developing Country: Costa Rica, Panama, Venezuela, Colombia, Ecuador, Peru, Chile, Argentina, Uruguay, Cuba, Republica Dominicana.
3.-Less developed country not Least Developed: Guatemala, El Salvador, Honduras, Nicaragua, Bolivia, Paraguay, Guyana.
4.-Least Developed country: Haiti.
As you can see, Haiti is the only one in the category of Least Developed Country. The Second Poorest Country in Latin America is Nicaragua and it's in the category 3.
In response to your answer, yes Costa Rica is a Third World Country.