In all my years of study and my own personal experiences.... Yes.
Each person has a specific astrological make-up. The natal chart is just like a thumbprint, unique to the individual.
The arrangements of the planets and their relationship to eachother based on the signs they are in, creates a dynamic that is this persons potential and persona (internal as well as external).
It can be seen through the natal charts, the dominating personality archetypes and that can indicate compatibility.
When using astrology in relationships, there is Synastry and Composite charts. Synastry compares two charts to eachother. Composite is a single chart created by using the two natal charts and putting the planets placements at the midpoint between the natal positions.
A sysnastry chart looks at the compatibility between the two where the composite chart expresses the dynamics of the relationship.