There have been several discussions on the power demand of the logcat event on various Tasker groups. It summed up as, Tasker doesn't make anymore demand than the OS does, since it piggybacks onto the system.
In the Tasker user guide, power usage
, is a list of contexts in increasing power demand. If you pair a power demand context with a much demand (e.g. time of day with gps location) you can minimize the drain