Yes, a server would be useful for this task, either a local (physical) server that you own or a server on a cloud computing service.
No, RStudio Cloud is a cloud service that provides you with an RStudio session, but it is not a virtual server where you can schedule a job, as an alternative you can set up your own server on a cloud computing service like (Amazon Web Services, Digital Ocean, Google Cloud Computing, etc), here is a nice blog post that explains how to do it.