If you have a modern version of PADS Layout, yes this is supported! The short answer is... Look under the Tools Menu for Import PartQuest Parts!
The longer answer...
1. In the PartQuest website, click your name and go to your profile
2. select "PADS Netlist without xDX Databook" as the current flow.
3. Download and install the PADS integration utility
4. Restart your web browser and PADS
5. Download a part. I tested with P1.0KBCTR-ND, double click the .pqz file to start it's extraction.
5a if prompted for a path, I create or use C:\PartQuest
6. From PADS Layout, Tools Import PartQuest parts. You many need to browse to C:\PartQuest\PADS_NetList
(C:\PartQuest was created in the previous step)
7. The decal or footprint will import, you will need to create a part from the decal.