Yes you can get sick from cockroach feces since cockroaches carry all sorts of diseases.
If cockroaches have made contact with any food or drink you have you should throw the food or drink out because it can cause you to get ill.
If you have cockroaches you should get rid of the cockroaches as soon as possible especially if you notice just a few because cockroaches will multiply fast and then it's much harder to get rid of the cockroaches.
Make sure to clean up any food residue and put food away so the roaches won't be attracted to the area.