Probably less mechanical impact than when you cut them mechanically, though

EDM works by micro-melting at a very local scale. This melted layer and the sourroundings areas will cool-down very fast again in the dielectric bath, but some modified microstructure will remain after cutting. In addition, inner parts could cool-down slowly producing micro-structural changes like for instance precipitation or stimulating other diffusion processes (with the corresponding decrease of the thermo-mechanical properties). This process is very unpredictable because it depends on the size of the sample we are cutting and obviously on the cutting parameters.

I recommend to do the solid solution thermal treatment after EDM cutting, in order to regenerate as much as possible the microstructure. If this is not possible, then use less-agresive EDM cutting although it takes a bit more time.