With Photoshop it's easy to see the conversion has been done. You simply open the file (as I did with the file I saved from LR). If you've set the RGB Color Management Properties to "Preserve Embedded Profiles" Photoshop will open the file and set the working space to that of the embedded profile. If the data hasn't been converted properly, it will be obvious! If the file has been converted with no embedded profile it will load as untagged and be loaded in your default working space (e.g. sRGB). It will look wrong. If you know what the profile is you can then assign that profile to the image, changing your working space to that profile. You can see the differences in the profiles by assigning between sRGB and DS profiles. You can also use layers with difference blend mode, to highlight the colour differences between the profiles. Another way to verify the conversion has been done is look at the pixel values. They will change.