Every photographer encounters this question now and then. I'm sure the more basic question—whether or not it's a good idea to carry a camera habitually—has been argued since the invention of reasonably convenient hand cameras. I'm also sure there is no proper answer to the second question: the choice is a matter of personal preference.
I don't carry a camera every time I go to the grocery store or the post office. However, as a full-time photographer without a day job or a daily commute, I spend a great deal of time out specifically hunting for pictures. Sometimes just for a morning, sometimes for days or weeks at a time. The picture above was made one recent evening, through the window of a pizza parlour in Watertown, New York, while I was waiting for my slice and salad to arrive. I was on a three-day expedition to find pictures, with absolutely no preconceived notions of what I was looking for.
This picture was made 26 hours or so earlier. I'd pulled into the convenience store parking lot to get off the road and use my cell phone. The picture just jumped out at me, so I shot it, then made my call. Taking blocks of time when my entire attention is devoted to finding pictures seems to work for me. Not carrying a camera the rest of the time also seems to work. Making the separation may help center my attention.