Bad idea. These drops will only mask the infection and can result in rebound redness with prolonged use. Use chilled artificial tears in addition to any other drop deemed necessary by your doctor.
Probably. Since most pinkeye is caused by adenoviral infection, the use of redness relied eye drops does not treat the underlying cause. While it likely does no harm and the lubrication may be comforting, caution should be taken not to touch your eye or lid with the dropper and potentially spread the infection to the other eye. Also, never share drops with anyone. The virus is very hardy and easy to spread!