If I am understanding what you want to do correctly there is no reason that you couldn't have all water to the sink come through the pump spout. You would need to tee in below the spout for the conventional flow---coming from one pipe already teed together with hot and cold. Valves would still be needed to control the ratio of hot to cold.
The hard part, without knowing exactly how the pump works, would be to cut out a section of pipe for the tee and get it precisely the correct length it was before. You might also be able to add to the pump rod instead of cutting the pipe that has the tee installed.
I am assuming that the suction part of the pump is at the bottom of the cistern, otherwise I doubt it could be done easily.
The hard part, without knowing exactly how the pump works, would be to cut out a section of pipe for the tee and get it precisely the correct length it was before. You might also be able to add to the pump rod instead of cutting the pipe that has the tee installed.
I am assuming that the suction part of the pump is at the bottom of the cistern, otherwise I doubt it could be done easily.
