"My house is near the café."
Translation:Мой дом возле кафе.
No. Дом is the subject here, so it's nominative. Have a look at the difference between personal, possessive pronouns and possessive adjectives.
All pronouns always REPLACE nouns. Adjectives are tagged on to nouns.
Мой is tagged on to дом (rather than replacing it), so it's an adjective (not a pronoun).
Adjectives follow the declension of their nouns - not the other way round. So мой cannot trigger anything in its noun. Instead, мой, as an adjective, follows the case of its noun, дом. Since дом is the subject if the sentence, it's in the nominative case. So мой is also in the nominative case.
Some English examples: https://www.answers.com/Q/What_is_the_difference_between_personal_and_possessive_pronouns