Re: Is this idiom correct?
It's rather long for a tattoo. "A gilded cage is still a prison" is a little shorter. Even so, I would suggest you talk to a lot of people already wearing ink for their view on such a long phrase. I think there's a reason most tattoo that consist of words are single words: Mom, or a child's name. All I can say is, it hurt so much more than I had expected it to, but once the first dot is in, you're committed.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.