No, you will not loose depth (although as Nimrod mentioned, a really tight pattern may loose you some of the responses).
I imagine a lot of people are confused on this discrimination vs depth thing: I'll try to explain as best I understand it.
When discrimination first came out, the circuits were analog. What they were were filter circiuts: low pass, or in the case of notch discrimination, band pass. These analog circuits caused some loss of depth for targets just on the accepted side of the discrimination setting. (This would be easier to explain if I had a graph of signal response to post).
Modern digital detectors actually run in all-metal mode continuously. They see all targets. They discriminate by not reporting targets that have been blocked out. This method has no inherent depth loss associated with the discrimination.
The above information is correct to the best of my knowledge. If someone else has different information, please let me/us know!
Louis