In the majority of cases yes, however in some cases due to the age of the stain or the carpet fibre type they may be damaged beyond repair. The quicker we get to a stain the better chance that we can remove them.
White wine will merely dilute the red, it would be better to use warm water and paper towels.
Unfortunately it is not possible to get all stains out as some are damage to the carpet's dye. However roughly 85% of stains we will be able to remove.
As a rule of thumb everything you put on your carpet you must rinse out, otherwise bleaching can occur. If you have a Wool carpet you must never use high pH cleaning fluids or rub the carpet as you can perminatly damage it.