Yes and no... It all depends on the context of your question.
If you're asking if it is literally part of the house, it certainly is. Just like a garage, a deck, or a porch is a part of the house.
However if you are actually asking if it is considered part of the living space then the answer is no, it is not considered part of the living space. The square footage of a home is normally based upon the heated and cooled living space. Even though a patio can be considered an extension of the living space it is not a part of the climate controlled area. Therefore it is not considered when calculating living space.
No, only living space is considered part of the house.
If the patio is attached to the building is it part of the building?