Air coolers for the win.

Doesn't look like corrosion, since that would likely be a blue/green color from the copper (you can see a little of that oxidation in the third pic), but it probably is a buildup of minerals as the main plate has slowly leaked fluid out the sides.

Should you use it?

It's leaking fluid. Unless you know for a fact it's using some kind of non-conductive fluid, it's a matter of when it leaks onto something more important, not if—probably your GPU, if not your CPU.

I'd guess it's a tiny leak and something in the heat transfer fluid can corrode copper when exposed to air. Copper turns blue when corroded, and the white buildup is probably the dissolved solutes from the fluid being left behind as the water evaporates.

Probably best to replace the AiO.