I don't see anything about negative reactions of borates with copper. Mostly copper will corrode from low pH and from very high oxidizer levels, especially in combination. Copper heat exchangers most commonly fail if they have tight U-bends as the rapid water flow turbulence accelerates the corrosion.
If anything, the additional pH buffering from the borates should help maintain the pH which can only help reduce corrosion rates, though in practice borates are often used in pools using hypochlorite sources of chlorine or SWG systems where low pH is not very common -- such pools tend to rise in pH which is part of the reason borates are used in the first place.