It doesn't seem that there's definitive evidence of support for the E38xx line or Bay Trail generally.  However, Silvermont, which Bay Trail is apparently based off of may or may not empirically have worked (http://www.insanelymac.com/forum/topic/294514-mavericks-on-intel-avonton/).  Apparently this caused an issue on Tonymacx86 a few years back - http://www.tonymacx86.com/mavericks-laptop-support/116372-installing-mavericks-bay-trail-tablets.html .