Yes.Fit events accept running and walking, and sometimes cycling and daily activities (for activity trackers). Make sure that your events are labeled this way and not as "treadmill", "mountain biking", etc.
If your miles are marked correctly with an accepted activity, go to your race progress page and make sure you have declared your device as the recording method for the race. If you see the words no device selected, click on the words no device selected and select your device from the drop down.
Please make sure to sync your device. Some devices like Fitbit go to sleep and need a sync to happen for us to receive the data.