Yes, a fever can cause water eyes. The reason why watery eyes appear is because the blocked tear ducts or excessive production of tears. On one hand, when your tear ducts are narrowed or blocked tears, it will not be able to drain away tears and as a result it build up the tear sac. When this tear sac appears, the risk of getting infection is increasing. The eyes will automatically produce a stick liquid and get the problem worse. This infection may cause nose inflammation as well. On the other hand, when your eyes are irritated, they will produce more tears than it used to do. When this happens, our body will tend to get rid of this irritant. So our eyes produce more tears. There are association between eye irritation and fever, so when you have a fever, your eyes will irritated at the same time. Then watery eyes appear.
