In theory, if 100% of the dissolved solids are removed by the RO membrane, no matter what the input, the output is totally pure water and will have a pH of 7.00000000000000000...
However, no membrane is 100% efficient, so there still will be some minuscule amount of dissolved solids that can affect the pH, and as kentuckiense mentioned, gases absorbed from the atmosphere can affect it as well.
The reason that pure water can be so corrosive is that it's unbuffered, so the slightest amount of dissolved solids can make it quite corrosive, if they acidify it. If they make the water more basic, your copper pipes are likely to build up a deposit of copper hydroxide.
My well water has a pH of 4.7 coming out of the ground, and we neutralize it by injecting potassium carbonate solution into the incoming stream. If I forget, I get pinholes in the copper piping, and if i overdo the concentration, I get nice blue-green copper hydroxide and carbonate deposits in the shower.