Yes, that is correct that you cannot install Pega Robot Studio and Runtime in a single environment. However, Pega Robot Studio does include Runtime executable which you can use to test the published packages to Robot Manager. This executable is in the instllation directory of Pega Robot Studio which by default should be in C:\Program Files (x86) \Pegasystems\Pega Robot Studio.
The purpose of the Synchronization service is to ensure that running Robot Runtime version matches the Studio version used to build and publish the package. This will be not be an issue in the scenario as the Runtime version is already same as Studio version.