Your Connect account is managed separately from your personal Gmail account(s), therefore the data and settings from these accounts will remain separate. Only data that you manually copy between the accounts will be shared (e.g. if you send a personal email to your Connect mail account).
Whatever account you log into first will be the default account for additional applications in G Suite (Groups, Drive, etc). If you want to use the same browser to monitor your Connect account and your personal gmail account, be sure to log into your Connect account first.