No. You can remove (with a bit of fiddling) it but to my knowledge you can't reclaim the space it takes (even if you could it would present other issues since it is much smaller than a 1-height widget).
Actually it is not, it is persistent and cannot be removed unless you use an alternate home screen replacement (like Nova Launcher). There is also a widget that you can place anywhere.
It seems to be based on the standard launcher, but allows you to customize a lot of things, including the search widget.