Yes, you will still be able to earn from your own cash back purchases, as well as the purchases of those in your network. The bonus challenges are there for those that wish to supercharge their earning potential to the next level, however they are not a requirement, and those that do not wish to complete them can still earn a healthy amount without meeting the bonus challenge conditions.
To earn from the main program, all you need to do is simply shop with your favorite merchants through the Fluz app, and grow your network through inviting or allowing indirect network connections to form over time. For a more detailed overview on how to unlock the full potential of the income derived from your network, see here.
While this more passive approach is still viable, those with the inclination to complete challenges will see a much more rapid increase in their monthly take home through the Fluz app.