To answer the question of the OP. I have never heard of pirated materials causing a normal person to be pinged by a warranty claim on storage, indeed it is rare even for companies to get pinged via such means (most of those tend to be bitter ex employee or some kind of audit). Second to that nobody has more than about 5 gigs of documents, photos and home videos, certainly not terabytes. Drive companies know this (some countries even tax them because of it) and thus if it gets around that they are shopping people... yeah their sales will likely drop off a cliff. It is not like it is their IP either (I assume you don't keep the manufacturing secrets and CAD data you stole from their servers on that drive).
For the most part though they will probably open it up, read the basic drive log to make sure it has not been dropped and look at the water labels to see it has not been sent for a swim. If a new caddy will do something you might get it back, if that is more effort than it is worth then they will probably just send one of the replacement units (an hour of engineer/technician time might be worth more than a simple replacement).
Impossible? No. Can even see a path that would not even be the plot of a cheesy film. Have I ever heard of it happening? No.
I got my first external about 16 years ago and was already a year or two late to the party (USB flash drives were just about taking off and sometimes it made sense to shove a CF card in a reader still), torrents had also just got really big and have been floating around circles like this ever since, before that as well actually, and following copyright cases for about a year less than that.
Did you drop it? Those external HD are really hard to break unless you get it wet or drop it. But to answer your question the repair guy probally won't care. If it is the OEM they are just going to send you a refurbuished unit.
My entire life is on my 5TB external HD I would go nuts if I cant access the data.
External drives are pretty susceptible to damage in my experience. Sometimes it is just the controller that goes, other times the jostling in the bag and lack of airflow means they die far quicker.
Still if your data is all in one place, never mind something as unreliable as externals, then probably best to get a backup of it if the data means that much to you -- data that does not exist in more than one location does not exist.