It will. Just take your time, don't rush through it. Use good painters tape, like that green frog stuff, or that other one that is blue. If you don't, you'll get thousands of little hairline leaks. Check the weather of course. And most important, get plenty of before/after pics to share.
Thanks for sharing BobThe method recommended.......works! I use an electric paint remover/heat gun. Use it on LOW setting and pay attention so as not to apply too much heat.
Since I don't have a heated garage, this seems like a job for this coming summer.