I t think so, libraries, and digital libraries as well as website of the university are very important for university accreditation and quality of teaching beside research. Therefore, these are key items for each university.   

When needed, I can't do without them. The nearest place to have hands on access with no login, no need for password to remember, no need for internet access, no WiFi bills to pay is libraries. No student can afford purchase of textbooks for all courses in a programme. Accreditation body and assessors are sympathetic to welfare of students. Libraries are ideal places to provide conducive intelectual pursuits and for scholastic research.

In the USA colleges and universities are accredited by geographic regional commissions/organizations.  In the northeast the group is called NEASC and can be found at: neasc.org

They have new standards as of 2016 for what is required of colleges and universities, and Section 7.22 discusses Libraries:

"The institution provides access to library and information resources, services, facilities, and qualified staff sufficient to support its teaching and learning environments and its research and public service mission as appropriate. "

The libraries is oof the most potent impact factor of universities for all specialzations in spite of the Internet dependency from hug no. Of students. 

Even if all the quality information and research published was completely Open Access (which would be great of course) there'd still be a role for specialists to help students and researchers navigate through the wealth of information available to find what was most relevant for them, and also to help evaluate it. So that's a good role for Libraries too even in a completely electronic environment

I do not think it is possible. Central Library facilities play key role in accreditation of heis in India. The NAAC which is a federal agency in India takes into consideration the key factors of Library facilities and its functioning, while accrediting the universities in India.