It could absolutely be a factor in the effectiveness.

Placebo is a highly effective drug.

I say this as an extreme evangelist of GLP-1s. Behavior modification and habit building appears to me to be a large part of it. Friends on it who have used to as a performance enhancing drug to change habits have generally stuck with newly developed habits even coming off the drug. Friends who used it as a magic weight loss drug largely returned to previous weights and poor health, even some maxing out the doses over time.