As I use tasks.org myself, I pretty much guarantee that you can. :) However, Posteo has to my knowledge no todo web app so you'll have to rely on your Phone or PC for ticking off stuff. But if you use the "Add to calendar" option you will definitely see them in the web calendar.
I also use K-9 and the default calendar and I haven't found a way to do that. But it's an Android limitation.
Perhaps something to look forward to when K-9 finally becomes Thunderbird for Android next month?