I haven't used Oracle in 12 years, but what you're describing does not sound like an Oracle issue. This sounds like an issue with the reality that R is single threaded. This means that while R is busy doing one thing, you can't do something else. R Studio waits on R before becoming responsive.
One way around this is to run your ROracle scripts as jobs in R Studio. However you should keep in mind that the way this works is it spawns a new R worker and runs your code in there in order to keep your main R session responsive. So objects from the job are not copied over to your current workspace. You will need to have your job write any results out to a file and then import those results in another R session in order to do things with them.