It would show up in a DNA scan or a blood-tissue scan. We don't have that technology in the clinic so far, but if it ever turns up or the wardens do something... at least you've got a warning. [ it's better than nothing at this point and she'd rather have martha know ahead of time than be caught by surprise. ]
I can. I've been in hospitals plenty of times with no ill effects. I've no idea what my blood might do to anyone else and I'd rather not find out the hard way here.