It's possible, and I think it will happen eventually, but I think we're getting ahead of ourselves with such notions right now. Not when my neighbor just got handed a death sentence (pancreatic cancer) or when I can't buy a reliable over the counter cure for planter's wart. I mean these are just two of the things we'd have to be master before we can start talking about biological immortality.

It's a little like the fear and loathing around AI. I'm really not worried about my computer overlords taking over when I can't even get the OS on my computer to behave rationally on a slow network connection, or when Windows still succumbs to the Blue Screen of Death, or when the latest software upgrade by my TV service provider slows their whole UI down threefold. Or just in general when I, as a lifelong IT worker and computer-literate person, end up throwing my laptop at an outside specialist in frustration rather than tear my hair out over such things.

Technological advances have to be absorbed and integrated and perfected, and any unintended consequences fully understood and dealt with. All of this takes time. And takes time no matter how desperate we might be to cheat death just a little while longer.