Yes it can be done. However please understand that having a not splitting is a totally irrelevant technical specification as the PDF is allready split to pages. The data will be split many ways before the process is completed in any case because that's how processing works. Split to disk or memory is the same thing and writing a PDF is assembling pages.
As for can it be done without doing manually. Yes naturally, all the things that can be done without extensive user input can be done automatically. So if the sequence can be described as do something well defined like pushing a button open next page.... then its not just doable its already done fully automatically. Extending it to do for each page on your whole hard drive was the sort of thing every single computer operator used to be able to do before the 80's. Its even easier to do today, but sadly we are loosing ground here.
Not knowing what apps you have available what os you use limits practical guidance. But basically you write a script that loops over each page, better yet any number of documents worth of pages. But the inkscapes trace module works from command line so writing a batch loop is not really hard.
What you end up with is a different thing. Personally id just ocr the thing dump text as text and vectorized only the critical parts. But this is the sort of things programmers make their money from.
The problem is not so much doing this as it is deploying it so it works on your computer.I know it is retarded to use a day to solve your problem and then use a week shipping it to you.