I suppose it is, but there are definite liability considerations, depending on what you are doing. You won't likely find this priviledge at a hospital, but more likely at free clinics. You don't need certification to obtain vitals and patient history; that's fairly innocuous, as long as you receive training and are supervised by a professional who has a healthcare license. In general, you cannot, however, provide any treatment or make any interventions without some sort of baseline healthcare certification under which you practice under a medical director's license; even then, your scope of practice is quite limited.
It's fairly easy to obtain phlebotomy certification, and many hospitals will training you on-the-job. Check with one you wish to work for and see if they are willing to do this. CNA is a little more time-consuming, usually taking about a semester, but will allow you to practice under a medical director's license, so you can do much more patient care.