Not in my experience. The Valheim dedicate server starts to eat up a lot of memory once you've explored like a quarter of the map as it tracks spawns and entities in the game.

One physical CPU core per person that intends to connect to the server is also recommended. The CPU is honestly probably fine, but if you intend to fill an entire server with 10 people, you're gonna have a bad time.

I have no experience with the game on a Hard Drive, my dedicated server is using an SSD. Can't say how that would shake out.

That being an HP OEM computer, it's probably a dead-end for upgrades.