Yes, viruses are substantially removed by reverse osmosis membranes. However, studies performed have shown varying viral removal efficacy, varying from 2 log removal (99% rejection) to 5.9 log removal (99.99987% rejection). This is believed to result from imperfections in the membranes. It can also be exasperated by mechanical or chemical damage which can result in a loss of salt rejection.
In a paper titled “Removal of biological and non-biological viral surrogates by spiral-wound reverse osmosis membrane elements with intact and compromised integrity”, the authors found a correlation between rejection of viruses and rejection of sodium chloride, where an increase in salt passage would indicate an increased passage of viruses across the membrane. The paper can be found at the following link:
http://people.ce.gatech.edu/~jkim/documents/WR%202004%20%5BVirus%20Transport%20through%20RO%5D.
See also:
When does it make sense to clean elements, and when is replacement the only option in high purity applications?
Does reverse osmosis desalination of sea water remove viruses from the product water?
¿La desalinización por ósmosis inversa del agua de mar elimina los virus del agua de producto?
How can we determine whether the membranes in our Reverse Osmosis system are damaged?