Yes, doing that method you describe (I have done it myself) will leave your source environment fully operational and without issue. Any subscriptions you have in the source environment won't fully copy over unless you also copy the Agent Jobs from source to target though. .... although that may be what you want.
And if you are going to a different environment, do you want them pointing to the production database? You may want to just forget the encryption key stuff and leave the data sources broken if you are going to have to change them all anyways. All that moving the encryption key over does is allow the new environment to use the saved password information.
But you may also want to take this opportunity to add all your reports into source control (Visual Studio). Then you can just deploy from the project to whatever target server you want. There are powershell methods around somewhere (I think DBA Tools) that can help with this, extracting all the rdl files to a folder, for example.