With DNGs where you've manually updated the preview, the color profile is embedded (as Andrew said) so if you delete the external profile from the disk, no problem.
Otherwise, the profile is obviously no longer available to process the raw file, so when you do try to process the raw file, a substitute profile will have to be used. The default substitute is "Adobe Standard", assuming it exists. (Of course, it is possible to remove that, too, so after that LR will pick the next external profile available, and if there are no such profiles available, it will eventually fall back to its built-in matrix profile.)
