It depends. It probably is a good idea to strip it down to the bare frame, clean and grease everything and build it up. I do that sometimes. I almost always take everything off but not necessarily all at once. It kind of depends on my schedule and motivation. Sometimes it takes me 6 months to get around to doing everything, if I believe the bike was fairly well maintained to begin with.
If it is a basket case, I would definitely strip it to the frame and rebuild it.
But then I only buy bikes that I want to ride, even though I eventually sell most of them for a small profit.