Yes. Breastfeeding can continue most illnesses and circumstances.  kellymom.com has a lot of information about what is safe when breastfeeding.

For me, mostly, it is more like no choice - Zoey is still an avid nurser at 17 months, and I could not imagine having to deny her just because I'm not feeling well. I do find that having to stop and nurse her makes *me* take a break even when I didn't realize that I needed it. I have found that I've been sick less - only once since Zoey was born - not sure if it's coincidence or luck :)

I had a day surgery (with general anaesthesia) back in May and did not stop breastfeeding. My surgery was at noon, and I was out by 4pm. Picked up Zoey from daycare at 5:30pm and nursed her - we didn't notice any effect on her.

Could it also be true that when you're sick, like flu or fever, its the time our bodies produce a huge amount of antibodies to fight it off and those antibodies are somehow transported through the bloodstream and into the mammary glands  and thus into the breastmilk?  And that its a good assumption that baby actually gets a boost in her immune system?  Would you agree?