if you're feeling ill i would advice not to go to the conference, besides my supervisor always told me, if you're ill stay at home! because you're going to make the rest of us ill.
no its not bad to miss a conference, especially if you're not even presenting!
your health is more important. conferences come and go. i never went to any conferences. although they are good, but its not the end of the world if you dont go
just tell your supervisor of the situation. and he/she will reassure you. maybe someone can go instead of you and take notes or whatever