It is possible to export rasters in ArcMap by right clicking the layer-> Data-> Export:
You can then click 'Use Renderer' check box to ensure the image you export uses the current symbology/rendering settings for that raster layer.
There does not appear to be any geoprocessing tools that match this 'Use Renderer' functionality.
I need to export over 200 images with these settings. I'd rather not do this manually. Is anyone aware of any way to automate this process?