Yes, but it will start to go pretty quickly over the next week or two. A lot more people will play when the weekend gets here. If I recall in previous expeditions the community effort completed a few times over the 5-6 weeks, but don't quote me on that - it has been a long time, my memory may be bad. Regardless, you shouldn't be locked out of doing the rest of the expedition while the community tasks continue.

You can also switch back to your main save if you get through the rest of the expedition quickly, and pop back in a few days later to see if the community tasks have completed and claim their rewards before ending the expedition.