It might. Any time a baby (or grownup, for that matter) is sick, her appetite tends to dwindle. Plus, baby could have lesions in her mouth, making feedings uncomfortable. It's okay if she takes a little less milk (and/or solids) than usual for a few days. If this is the case, consider pumping after feedings to help keep up your milk supply while she's sick.
Babies don't often become dehydrated by refusing to drink. (Dehydration is usually due to vomiting or extreme diarrhea.) So don't worry unless she's showing real signs of dehydration, like wetting two or fewer diapers in 24 hours.