Being engaged in

Does "his paintings as being engaged in his difficult relationship to his father" mean "his paintings reflected and represented (were inspired by) his problematic relationship with his father"?

Context:

Ernst often referred to his paintings as being engaged in his difficult relationship to his father, but the incorporation of Freudian elements gives this painting an impersonal resonance that opens its meaning to other
people, not just readers of Freud. The rationale for this is of interest. In an episode of the TV series Imagine on the theme of art and play, Adam Phillips, a contemporary psychoanalyst, suggested that the artist socialises personal trauma in the artwork, that artists transform something from childhood into a form other people know something
about.