Yes, it absolutely can, it’s super easy! Just swap your Minecraft .jar with Paper and it’ll do the rest. It’s a tiny bit harder to go back, but only marginally.

Out of the box, aside from huge performance benefits, Paper is virtually indistinguishable from vanilla, but it also opens the door to a whole world of easy-to-use server-side plugins.

Edit: (you should still make a backup before swapping, just in case)

CPU intensive servers like Minecraft are where you start to run into problems with older hardware. If it’s just you on there, a 10 year old CPU is fine, but if you’ve got a few friends, the server may start to struggle to keep up.

Not sure how recently you ran this, or what all your were running, but in the past couple of years Paper has hit some pretty major milestones in unlocking threaded processing. Barring some sort of spammy 0-tick redstone nonsense or over the top plugins, I’d wager a Raspberry Pi 4 could handle up to about 5 or 6 friends without seeing any TPS dips. Its really remarkable how far they’ve pushed performance recently.

Could I get a larg HDD and ad it in an enclosure to the Mini PC to handle the media volume?

Like an external USB drive? Absolutely.