Growing up the rule of thumb was "fever means no milk". I have done the same w/ my kids even my daughter who LOVES milk.
Do push the liquids though for two reasons...first, you want to be sure they stay hydrated and secondly, when they have a fever and don't drink the fever thrives and goes higher so staying hydrated will actually help keep the fever at bay. No, it will not necessarily get rid of the fever but it will help keep it from rising. As the fever rises, they tend not to want to drink and then they get dehydrated and causes the fever to rise more.
When my kids are asleep, I do not wake them unless I have to. Our doctor told me that the best medicines in the world won't make someone better if they don't get rest. If the fever is too high, certainly takes steps to lower it even if that means waking them enough to give tylenol or motrin.
Here are some steps to help bring a fever down...you may know most already but here goes: push liquids, ice pops, etc; don't over bundle; cool rag or ice packs on back of neck/wrists; and tylenol/motrin as needed.