This is not really an answer to your question, but I want to say that "I" have never seen such an application on CRAN. What you will see on CRAN; however, are packages that interact with an API to get data. Is it possible to explore that route in your case?
The CRAN submission policies don't specifically prohibit a package that relies on a database connection, however, there are a couple of caveats to this.
From the CRAN policies:
Packages which use Internet resources should fail gracefully with an informative message if the resource is not available or has changed (and not give a check warning nor error).
Packages should not write in the user’s home filespace (including clipboards), nor anywhere else on the file system apart from the R session’s temporary directory (or during installation in the location pointed to by TMPDIR : and such usage should be cleaned up). Installing into the system’s R installation (e.g., scripts to its bin directory) is not allowed.
Downloads of additional software or data as part of package installation or startup should only use secure download mechanisms (e.g., ‘https’ or ‘ftps’). For downloads of more than a few MB, ensure that a sufficiently large timeout is set.
Given those policies above, your package should pass a CRAN review as long as when the database is unavailable the package gives a reasonable error message, you're not leaking any information about the user in the database request, and your requests are encrypted.