"evoke connections" is correct and usable in written English.
You can use it to describe when someone or something helps create a link, connection or relationship between two things. For example: The music at the concert seemed to evoke connections between the audience and the artist.
To a former colleague of Mr. Ruble, his tax shelter work evokes connections of another kind -- of a lucrative and legal "hub and spoke" model that Mr. Ruble developed for marketing and distributing mutual funds and common trust funds through multiple outlets.
As the scaffolding surrounds the most essential elements of the structure it evokes connections to security, age, and preciousness.
The movie is a protracted erotic tease that evokes primal connections between sex and violence, masculine and feminine.
Moments before losing their sense of smell, the victims have fits of inconsolable grief that evoke the connection between smell and memory.
I know this trailer is meant to evoke a connection with all the dumb shit I remember from elementary and high school, and it does.
These applications are evoking new connections between mathematical subdisciplines such as algebraic geometry, algebraic topology, differential geometry, differential topology, dynamical systems theory, general topology, and singularity, and stratification theory.
Some coproducts, such as Direct sum and Wedge sum, are named to evoke their connection with addition.
Today the Dreyfus affair is still constantly evoked: in connection with the death of David Kelly, Guantánamo and the Iraq war.
"This is hard work," she said, again evoking "a connection to my African background," adding, "I watched my mother work so hard in this country".
She is often evoked in connection with the sympathetic and radiant portrayal of Violetta in La traviata (The Fallen Woman a rough analogy, to be sure, for Violetta the courtesan had fallen a great deal farther than Strepponi the singer).
