、、。
Whether they are conscious of it or not, human beings continue to pursue happiness.
Literal
Human [topic-は], self [by-で] that [object-を] is-aware-of [quotative-と] not [quotative-と] regardless-of-にかかわらず, happiness [object-を] continue-to-pursue-[polite-ている].
Philosophical/essay register. The clause ~しているといないと is a formal binary 'whether X-ing or not X-ing,' using repeated quotative と to list the two alternatives. ~にかかわらず 'regardless of, irrespective of' takes a preceding noun or clause and rules out its relevance. 追求し続ける is a compound formed by attaching 続ける ('continue') to the ren'yōkei (masu-stem) of 追求する — a productive auxiliary pattern.