I'll just reply to my own question and say Yes, you can. Way to go, me!

Care to share what your solution to your own problem was?

It's really just a matter of being able to read the data correctly when trying to enter in a data field. In my case, I had two tables of data. One was direct base data and the other table was my synced data from an outside base. My PDF generator extension was linked to the first table but I needed data in there from the second, synced table. So if you link the first table to the synced table and open up the lookup fields you want in your PDF, the data will be there to enter into the PDF fields. 

Heads up that the fields might look "hidden" - but if you squint your eyes and look real close, your linked field should be there as a dropdown that you just have to click on to open up.

I was getting hung up on adding data directly from the lookup field instead of through the linked field and THEN the lookup field. I'm not sure any of this makes sense, but I will say that it's incredibly cool that it works.

Yes, this is possible with The PDF Maker (https://airtable.com/marketplace/blkfNaV2eti4YuIVd/pdf-maker-bustbrain-labs) 

You can absolutely use data from a synced table in your PDF template. Just make sure that the fields from the synced table are properly mapped using the placeholder format in your template. If the data isn't showing up, double-check:

• The placeholder names exactly match the synced field names

• The synced data is fully loaded in the triggering record

• You’ve selected the right table and view in your automation

Every new record or update can trigger PDF generation!
 

Here's a detailed guide to help you:
How to create a template in PDF Maker using our Airtable extension