@burcidi-- Probably not. I think those side effects are most probable in people who take high doses of naproxen regularly and also drink on a regular basis. So those who are taking this drug every day and those who are suffering from alcoholism are at increased risk.
If you're taking over-the-counter naproxen, it's usually 200mg of naproxen per tablet. So if you only take one or two tablets per day and don't drink daily or heavily, you're probably not going to suffer from gastrointestinal side effects. But then again, there is no guarantee, so it's a risk to use naproxen and alcohol together regardless.