the implication when given [a cellphone] by your employer is that you should always be doing work.
Yup. If it gets to the point where an employer expects me to carry a phone (for other than a short-term support rotation), I'll be renegotiating my salary, billing them for being on-call 24/7.
I had a company give me a pager. The batteries ran out, and I left it on a shelf at home for the next two years. Not once did anyone try paging me (pages got sent to email, too). When I left the company, I handed it back, dead batteries and all.