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2 output pins in parallel? maybe, but you can not short-circuit them together: if during the setup or a transition one pin is high and the other one low (even for few microseconds), your Arduino is gone... it may work with a couple of diodes, but then the transistor is cheaper and more efficient (diodes have a voltage drop of 0.7V, a saturated BC547 a Vce of just 0,18V)
Nice idea, just a comment: the relay you are using (as I can see from the picture a JQC-3F-5V) needs a current of about 65mA to be activated, while the max output current into/from any Arduino output pin is 40mA. I suggest to drive the relay through a transistor (i.e. BC547)