Not necessarily. It could imply common design rather than common ancestory.
Cordially,
Common design that across the range of genomes catalogued matches the expectations of common descent. A Designer who only apparently designs in nested hierarchies that appear (from the fossil record) to be modifications of earlier nested hierarchies. Yeah, right.
A designer doesn't have to match the expectations of common descent, yet the lunatic who designed life on earth apparently did so, for unfathomable reasons, according to you. If you want a design hypothesis with legs try millions of teams of competing designers, all starting with the same basic template, with the objective of destroying/subverting each others designs, and only allowed to work with successive slight modifications. A celestial God-game or a Raelian management training exercise. That is a design hypothesis that matches the evidence, but curiously we don't see that one coming from the design proponents.