Before you read my response please know I am studying Electrical Engineering and although you cover fluid flow in thermodynamics I have not taken fluid mechanics.

From my understanding the short answer is yes they would reach a higher floor; BUT there must be a very specific set of start conditions. If one of the supply pipes puts out even a little less pressure I believe that backflow would occur resulting in failure. This is also a situation equated to circuitry where amperage is the flow of water, when you split a current into two wires it undergoes voltage division and when you bring it back together they undergo voltage addition. I feel like this would be like taking two separate circuits and connecting a wire from one to a wire from the other. If the conditions are not correct you would draw no current or you would create a flow from one to the other.

Just to restate though I am not experienced in fluid mechanics.