Yes, this is possible. To see how i and s influence the outcomes Y over time, see our Topic 3 Short Course video and handout, slides 96-98.
For effect calculations with growth, see the article
Feingold, A. (2018). Time-varying effect sizes for quadratic growth models in multilevel and latent growth modeling. Structural Equation Modeling: A Multidisciplinary Journal. DOI: 10.1080/10705511.2018.1547110