Depends on the bettas personality.
You would need to have the cardinals first, so he is therefore entering their space, and doesn't class the tank as his own - gives you a good head start but it really does depend on him.
Even if he does tolerate them, look out for signs of depression or general 'sulking' many say bettas are much happier fish on their own.
My veiltail is solitary, although my plakat has black neons as tank mates.