I keep meaning to do this, but every time I'm getting ready in the morning I talk myself out of it ... and then regret not wearing a diaper by mid afternoon when I need to go try and find a washroom ...
As someone who works in the field of emergency medicine/health care, it really isn't a big deal. If you're conscious and alert, we'll likely ask at some point, but saying "I have bladder problems" will be the end of it.
I don't go out diapered very often, but when I do, I make sure I'm pretty well concealed. I'm sure if someone was looking really hard they might notice, but beyond that, my diapers stay well hidden.