As long as one has reserve alcohol; it should not matter on dry/wet days! As for drinking in public; remember that Goa is very cool at that. However "when in Rome, do as Romans do!".
Dry or wet is solely a State decision. In Tamil Nadu for example Republic Day like May Day is very much wet day, on the other hand Mahavir Jayanthi is a dry day in TN whereas in other States like Haryana(Gurgaon)/Delhi it is wet!
" True love means the fight has disappeared, the two have become one. Their bodies exist separately but their being has mingled. The boundaries are lost, there is no division. There is no ‘I’ and no ‘thou’, no one exists" - Osho
Republic Day is NOT a dry day in Goa. All liquor stores, bars and restaurants will be open as usual. No need to bring anything with you. The only annual dry day in Goa is 2nd October (Mahatma Gandhi's birthday).