Not exactly.
Signs are the personality features and Houses are the "area of life" features.
The facet of the personality given by this Planet in this Sign is expressed in the area of the House.
The third House is related to Gemini (Mercury, books, communication, trade...), in relation with the way of thinking or move.
Moon in Cancer in 3rd => intelligence, imagination, traditionalism
The 9th House is related to Sagittarius (Jupiter, studies, religion, travels...), in relation with studies, travels...
Mars in Sagittarius in IX => adventures, religion conversion... for a woman it can lead to a relationship with a foreigner, a professor...
But,
Pluto transit cases , there is a link between low Planets and the House pointing the Sign they rule.
Jos Astrology index