The dead don't have circulatory systems, so injecting them with anything would have no effect.
When stabbed, the walkers bleed, so they clearly do have a circulatory system. Their muscles still work, so they have to be getting oxygen from somewhere, and it has to be through the bloodstream, however impaired that might be.
Quinn, who is supposedly fluent in French, introduces Isabelle but pronounces her surname as 'Carrier' (pron. 'kahree-ay') but it is 'Carrière' (pron. 'kahree-ehr').