On iPhone/iPad, can you view a PDF sync'd in iTunes?
Yes you can do this but the mp3s and PDFs are two distinct things that need to each be setup for syncing separately. 

So, sync your podcast/mp3s like you always do. Then you need to tell iTunes to sync your PDFs through the books tab when you have your iPhone/iPad plugged in. They will sync to your phone as a book and be visible in the iBooks application.

Unfortunately, that's just the way it works. You won't be able to view the PDFs in the iPod application on the phone, just through iBooks.