Yeah, search box in the header is pretty straitforward, and there are a couple ways to do it. The cleanest way would be to add a search control to the header. A slightly easier way might be to use a content column. Either way will require some reworking of styles for both the search and header.

Side note: I think in doing something like experimenting with moving the search, it would be a good idea to make it as flexible as possible. Meaning, that you can quickly remove/move it without having to rework too much. Since different stores are geared to different demographics, obviously, many merchants may see a decline in conversions when making the search input part of the header or in a prime spot on every page, while others might see an increase or no difference at all. So whatever you do, keep a close eye.

Have never messed with openCube.