If I have a healthy immune system, would that shorten or lengthen the period of time before I would show symptoms of a stomach virus?

If you heard about the sickness bug called noro-virus going around in the Uk a while ago, that started like a stomack bug e.g., stomach cramp and extreme aching in the stomach, thats how it normally starts and then normally goes on to being sick, after you were sick though you felt much better, the more healthier your immune system is the less likely you are to actually get the bug.