Is it possible to import a PDF with vector layers into MapInfo as vector layers? If yes, how would I go about doing this?
Well, not directly but it could be done with some workarounds in terms of format conversion with other software.
If your PDF contain vector data then this process goes usually via some PDF to DWG/DXF conversions and then importing results into MapInfo.
Results could vary from very disappointing to good, which depends of your goals and software and always expect additional work afterwards (cleaning, styling, etc).
I was doing this conversion mostly with Adobe Illustrator but you can find a many other converters which are free.
After exporting you have to georeference newly created drawing, so you should have to know coordinate system and several known points.
This is the answer that can also help you because it is very related to this: