If I joined the exercise, but were not active in it, will my time in-exercise still be counted?

Yes, active time in-exercise will count for as long as a participant is connected to the exercise.

However, if multiple participants of the group are connected to the exercise at the same time, (e.g., between 1pm and 2pm), then your group's active time will be recorded as the time of one participant (i.e., one hour in this example).