Docker images can be used to create an environment for a certain project or analysis. However, the use of Docker is orthogonal to RStudio Package Manager. For example, inside a Dockerfile for an R project you will normally see a line that installs R packages, e.g.,
RUN Rscript -e 'install.packages(...)'
This installation step benefits from RStudio Package Manager in the same way that non-Docker users benefit from RStudio Package Manager.