Company culture is an important factor when considering whether or not to make your feelings or intentions known, but I would put more stock in the personality of your boss.
I know of two people under the same roof at my company who took the two different approaches to this situation.
Colleague A told his boss that he wasn't happy, and his intentions were to look elsewhere. He was scolded, given less fun tasks, and generally treated with contempt. The worst part was that he didn't manage to secure a replacement job for almost a year later.
Colleague B told his boss that he wasn't happy, and his intentions were to look elsewhere. He was treated with empathy, asked if anything could be done to make things easier etc...
Same company, same culture, different outcome.
Unless you do actually want to stay at this company (which it sounds like you don't) or that you believe that your boss will treat your concerns with empathy and provide genuine support or advice, I don't see any reason that you should tell your boss or the full truth as it runs the risk of being treated unfairly in an already unfair environment (paraphrasing your words). You list policy as the main reason that you don't like your job and moving to another internal role won't be any different. The same policies will more than likely be rolled out there too.