Can OpenLayers layers in QGIS have transparency?

There is no transparency for OpenLayers layers. My usual work-around is to put a layer with a big white transparent polygon on top.

Background map layer transparancy can be changed if you use the QuickMapServices plugin instead:

You can in fact change the transparency or opacity of openlayer rasters, by amending the openlayer plugin html file.

For instruction of how to edit the html file, please see this link: http://lists.osgeo.org/pipermail/qgis-user/2012-February/015648.html