My wife used a visa for some time starting before she became a British citizen and continuing well after she had it. She never had a problem with OLCI beyond the normal inability to print BPs yourself for LCY-JFK. After getting fed up of carrying multiple passports each trip old one (with 10 year visa), new one and British Passport, she switched to an ESTA with her UK passport.
However whilst using the visa OLCI worked fine.