Yes. Amazfit Tools was designed to work in parallel with original Mi Fit application. You can use Mi Fit for daily steps and sleep statistics and Amazfit Tools for another features that are not available in Mi Fit (button control, button profiles, reject / answer incoming call, automatically send SMS to rejected caller, idle alerts, repeating reminders, hourly chimes, filtered notifications, specific contact and contact groups notifications, widgets, automation plugins, missed notifications, power nap, emergency calls, continuous heart rate monitoring ... and many other features that you get only with Amazfit Tools).
In case you have sometimes troubles synchronizing Mi Fit with your bracelet, this is caused by an error in Mi Fit application and it is not related to Amazfit Tools itself, this happens frequently even on iPhone Mi Fit or when you are using Mi Fit application only. Try closing Mi Fit application (or force closing it in your Android device) and opening it again - it usually synces correctly afterwards. Please also make sure to always use the latest Mi Fit application from Google Play store as syncing problems might be related to you using different (not from Play Store) Mi Fit versions.