Unfortunately, for now, the answer is no. All NROC Courses require a Learning Management System (LMS) that supports IMSCC content imports. Additionally, both NROC Developmental Math with PreAssessments and NROC English require an LTI connection to the NROC Course Manager. Google Classroom does not support either of those technologies as of the publication of this article.
Google Classroom is a way to manage web-based content (links), specialized apps, and Google's own tools for the classroom, but it does not allow for the import of course content via IMSCC files, nor does it support LTI connections. Google Workspace for Education may eventually support these features, but until then, it is limited in its ability to connect with external tools.
Until Google Classroom supports these industry standards, NROC courses will remain incompatible with Google Classroom.
NROC courses can be installed in standard LMSes that support IMSCC and LTI, such as Moodle, Canvas, Blackboard, Sakai, Schoology, and D2L.
NROC does not make any recommendations about which LMS you should use. However, if you are using Google Classroom because it is free and would like a free LMS that supports installed NROC courses, Canvas may be a good platform for you to provide the NROC coursework to your students. You can use still Google Classroom to manage your classroom content and provide a link to the course(s) in Canvas from within Google Classroom.
For information about Google Classroom and EdReady, please see this article.