Sometimes yes. The bacteria that causes food poisoning can live in your gut a long time after your initial infection and given the right gut conditions, can multiply again giving you a bad stomach and all the food poisoning symptoms.
Bacteria will feed of sugar and carbs.
If you eat some live yogurt or start taking some Acidophilus caps, then this will help to rebalance the good bacteria in your gut and help clear any infection. Keep them in the fridge and take them twice daily on an empty stomach.
I don't know whether you have a bad stomach at the moment? If you do you may like to try this. Take some Acidophilus and take 4 tablets daily to flood your system with the good bacteria, thus washing out the harmful bacteria. By flooding your system with the good bacteria, the Acidophilus acts like an antibiotic. Try this for about 4 days and if you start to feel better, cut it down to two caps daily.
A friend of mine told me about this and the last time I had a bad stomach I tried it rather than taking antibiotics and it worked. I took 4 Acidophilus daily for about 5 to 7 days and then cut back to 2 caps daily thereafter and my stomach was better within about 3 days.