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).

How to remove it (not without complications): http://www.addictivetips.com/mobile/how-to-disable-hide-goog...

You can indeed reclaim the space with, for example, Nova Launcher. My home screen has 5 rows, as a result, and no spacing issues or anything.

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.