Will previous activities count?

Whether or not to backfill previous activities is an option that the challenge administrators set. 

When setting up a challenge administrators can decide whether to backfill previous activities. If backfilling is turned on, a participants previous activities, logged before joining but after the start date (max 60 days), are automatically added to the challenge when they join. When backfill is not active, then any previous activities are not automatically added to the challenge. If a challenge lasts longer than 60 days, then Challenge Hound will only backfill 60 days worth of activities.

You can always see when you joined on the main challenge dashboard:

Why disable backfilling? Sometimes administrators run more than one challenge at a time and want participants to complete them in order. In this case, backfilling is turned off. For example, you have two different challenges all starting on January 1st and run the whole year. It is possibly for participants to complete both challenges independently. A participant signs up for the first challenge, then completes it. The same participant then signs up for the second challenge. If backfilling is on, then all activities applied to the first challenge will immediately be applied to the second (probably not what the participant wants). With backfilling off, the participant starts challenge two at zero (even though they've logged previous activities) and can complete challenge two without double dipping.

Backfilling can also be turned off if a challenge administrator just doesn't want participants adding activities before joining. For longer challenges backfilling can shoot new participants up into the ranks out of nowhere, which might be undesirable.