RStudio Connect is a publication platform for deploying content built in R and Python to share with a broad audience. R users may want to develop content (like Shiny applications or RMarkdown documents) using renv and then publish that content to RStudio Connect. This is a supported pattern where renv is used to manage the local project environment and then RStudio Connect recreates and manages the deployment environment.
The RStudio IDE includes a button for push-button deployment to RStudio Connect: 
When this option is used to deploy content to RStudio Connect, a manifest file is automatically generated and sent to RStudio Connect describing the project environment. This manifest file will reflect the project environment create and managed by renv. The renv generated .Rprofile file should not be included in deployments to RStudio Connect.
When publishing content to RStudio Connect programatically, it is necessary to generate a manifest file describing the project environment. This can be done with the writeManifest() function from the rsconnect package. When using renv, the only thing that needs to be considered is that rsconnect should be installed and executed from within the renv environment so that it recognizes the local project library when generating the manifest file. As long as rsconnect is run from within the renv created environment, it will capture project dependencies from the local renv library. This can be accomplished by opening the project in RStudio or by starting the R session from the project root directory. The renv generated .Rprofile file should not be included in deployments to RStudio Connect.
RStudio Connect uses packrat to restore project environments on the RStudio Connect server. This should have no impact on how the user develops content for RStudio Connect. It is not necessary for the user to use packrat instead of renv when developing content, as the environment management tool used locally has no impact on the tools RStudio Connect uses for environment management. Therefore, there should be no concerns with using renv to develop content that will be deployed to RStudio Connect.