DVD Shrink handles the basic copy protection known as CSS encryption, so even if you can copy a DVD using DVD Shrink, it might still be a copy protected DVD.
I recently backed up all of my DVDs, and a small percentage did not have any CSS encryption - even fairly new DVDs. Most of them did have at least CSS encryption, however.
If your DVD collection is not mostly main-stream movies, the percentage of non-protected DVDs could be higher.
In other words: Most but not all mainstream movie DVDs are copy-protected with CSS encryption and sometimes more difficult protection schemes, while for other types of DVDs the chance that they are not copy-protected may be higher.