My understanding is that there is some evidence that Alzheimer's is transmissible (e.g. higher rate of incidence in caregivers and neurosurgeons), but more study is needed.
https://www.newscientist.com/article/2151909-alzheimers-may-...
So while wiring together two bloodstreams is a bit extreme, and likely to result in most things being transmissible, there's nonzero evidence that you can have a bad day from a blood transfusion.