There are at least some situations where this could be valid medically. However, they would generally involve cases of organ failure requiring some form of dialysis like kidney failure or liver failure so the point would be to remove blood products from the patient containing the toxins that the liver or kidneys would normally remove from the blood and replacing them with clean versions. In that case, you're basically using other human beings as a dialysis machine, just in installments. Of course, for it to be useful, you would need to have a lot of donors who donate very frequently and you would need to do a very large number of exchanges. Otherwise, you could use a single donor in something like a traditional dialysis setting and pump blood out of the patient and the donor, run them through separate filtration and centrifuge processes, producing different sets of blood components, then put some of them, like red and white blood cells, back into the person they originally came from after mixing with other products, like plasma coming from the other person. That way you could use the kidney and/or liver from another human being as a replacement for a non-functional organ in another human being. In some ways, I expect it would work better than traditional dialysis machines in some ways because natural organs are self-regulating and require less guesswork and estimation than dialysis machines to achieve homeostasis and also because they remove more things and do it better. Of course, they still could not replace functions like producing bile (since it would not travel to the patient through blood), or regulating blood cell production as the kidneys do since the kidneys regulate that based on how many red blood cells there are so hormone production would be based on the high levels in the donor's blood rather than the low levels in the patient. Of course, I suppose there still would be more red cell generating hormones in the donor's blood anyway, so that should cross over and stimulate red cell production a little in the patient. Also, you could reduce the red blood cells returned to the donor during the session to match the patient and, over a long enough session, the donor kidneys would produce more hormones... In other ways of course, replacing it would probably represent an unacceptable risk of immune reactions in both patient and donor, even with separating the blood into components and only transferring some of them.
So, there is a situation where you could use another human (preferably a young, healthy one) as essentially a piece of medical equipment, but it would probably mostly be better just to use the actual piece of technology if available since the pros come with some potentially serious cons. As far as rejuvenation goes... There have been studies in mice that do show an effect from blood from younger mice into older mice. Of course, though I don't recall all the specifics, chances are that those mice were very closely genetically related (as in the product of multiple generations of mice born to cousin-siblings) if not outright clones. Plus, of course, they are mice which, among other things, have very short lifespans as well as not necessarily having analogues in humans to their biological reactions. Ultimately, there may be health benefits (along with some risks), but any effect is likely small. There is definitely no vampiric fountain of youth here.