The short answer is no, because the block is not aware of which section the user happens to be in at the moment, so it can't limit its display to just that section. It sees the completion statuses of any items in the course it's been set to track.
PB is being replaced by the newer Completion Progress block. You might check in that forum https://moodle.org/mod/forum/discuss.php?d=332078 so see if someone has asked for a feature like this.
It could certainly be possible to allow the user to select their "current section" to focus on in the block and show only that set of activities. That would make a nice enhancement.