If I had the headstock tied, there's no telling what kind of shape my necks would be in. I'm not known for playing gently, my guitar tech said I was really rough on a neck. It can also depend on what kind of guitar it is, and what kind of neck it is.

A one piece neck will be stronger, but it still seems like it would pull on it some. I pull on the neck sometimes for effect, and it doesn't take much pressure to lower the pitch of the strings.

Playing rhythm it wouldn't be as noticeable, but playing leads it probably would. You can put it on anyway you want, but make sure it's a nice wide strap. A sewn strap from multiple pieces wont last long before threads start to unravel and other stuff too.

JD