No. Once you install and activate your <em>press theme, your Genesis theme or other pre-made theme won’t interfere. You can choose to leave those themes in your Theme library, or remove it if you wish (we only recommend deleting a theme once you are 100% sure you don’t want it anymore).
If you have any plugins specific to your old theme, once your <em>press theme is installed, simply head to Plugins in your WordPress dashboard and deactivate these. You can delete them once you are sure you don’t want to switch back to your old theme (which we hope you won’t!).