This work discusses the impact of power consumption on the test time of core-based systems, when an available on-chip network is reused as test access mechanism. A previously proposed technique for the reuse of an on-chip network is extended to consider power consumption during test, while minimizing the system testing time. Experimental results with the ITC'02 SoC benchmarks show that although power constraints can preclude the full exploration of the network parallelism, this platform is still a powerful mechanism for the system test time reduction at a very low cost.