Is there a workaround?
Connex runs on a scheduled basis and there is no need to sign in to run the sync. You can instruct Connex to email a daily copy of the log. For more info, read this guide.
Can this be done?
Not at this time. QuickBooks will only allow one user at a time to sync with the same app and company file. Your Connex settings, rules, and tax mappings are associated with a user name and not a company file.