Right now there is no way to accomplish this with PDF Explorer by itself, but I may add it to the
My Scripts API in a next release. It would then be possible to batch script process each of the PDFs you wanna check, and put a flag in a custom metadata field that you may then use, from the grid, to select the files by that "has bookmarks" property. Or the script may actually automatically execute the operation you need to do on these files with/without bookmarks.
If you have Adobe Acrobat professional, you may already create a PDF Explorer My Script to accomplish this functionality. If that's the case, let me know if you need help with the script.