If management won't let you understand enough of the business to do so, I sympathize, I've been there. But if you're allowed to understand the business and are expecting someone else to come up with the innovation, you just need to get your shit together and be an engineer.
It sounds like you're implying that to work on innonvative projects one has to have the mind of an entrepreneur. While it's not a bad mind to have I don't think utilization of ones skills in a meaningful and interesting way should depend on that?
If you like the business but don't like what you're doing, can that change soon? If this is the deciding factor, why not phrase it that way to whoever can make that decision? Nothing to lose ...
If you just want to leave the company in general, than isn't your answer "yes?"