If the germs for the cold, flu, or cold sores are present on the eucharistic cup, yes. The precious blood does not inoculate a cup from the presence of airborne germs that cause illness. Reasonable care should indeed be used to clean the cup between communicants. If there is an epidemic illness, it may be prudent to only distribute the host and omit the cup until the epidemic passes. A full Communion is received under one or the other eucharistic species.
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