What does Hashirama mean by the effects of the chakra rods?
While people do regenerate under Edo Tensei, the process of regeneration can be slow and tedious. Madara has reached new heights and can attack at any given moment. Hashirama knows his chakra circulation is obstructed and it could take a while for him to heal fully. Thus, he is giving Sasuke this precaution along with a jutsu.

Refer to Minato's statement below. Also recall how Minato lost his arm and still hasn't regenerated yet. Hashirama knows that if Madara acts quickly, he won't be able to stop Madara.