If the city A harbor to capital harbor forms a city connection, city A gets the RR bonus - they don't have to be on separate land masses, but there does need to be a sea path for the city connection to form. If there is no city connection by harbor (perhaps ice blocks the path from one side of the continent to the other or maybe too much fog or AI/CS borders block the path) then forming a plain road connection between city A and your capital is NOT good enough. You either need an actual RR connection or the city connection has to be through (I.e., by means of) the harbor connection. If you have a good harbor connection, the fact that you might also have a plain road connection between those same cities is irrelevant.
Whether you have a plain road connection, a RR connection or a harbor connection or multiple connections (such as both a road and a harbor connection) will not affect the amount of gold generated by the city connection (there is no stacking if you have multiple ways two cities are connected). But it will affect the profitability of your connection, since roads, RRs and harbors have different maintenance costs. So, if you have a good harbor connection, you get city connection gold and the RR bonus. If you also have a road between those cities, you get no incremental gold; you just have maintenance cost of the road segments. If you want the road for military purposes, great, but be conscious of the cost.
Note also that automated workers apparently don't know anything about harbor connections and will insist on also building roads between already-connected cities if you let them. (Reason #483 why automating workers is a bad idea.)