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: