NAS hard drives are a bit slower than normal drives which are also slow too. So running the game on that kind of hard drive isn't recommended, but I'm not even sure you can host a game on a NAS device which is what I'm assuming you're referring to.
What I would recommend, is to host a dedicated game on a separate computer (anything quad core or better with 6GB of ram or better should handle it just fine, does not need fancy graphics card at all). This allows you and your brother to play any time separately or together and you can leave it active 24/7 if you wanted. I think you can have it LAN only, but if not, just password protect it and you'll be fine. Because it's just the 2 of you, you don't need a powerful computer to host the game. And by host the game, I don't mean load the game the normal way either, I mean there's an actual way of making a dedicated server. Simply go into Steam, click on Library / Tools, look up "7 Days to Die Dedicated Server", install it and run that on a separate computer. If you have a really powerful computer, you might be able to get away with hosting it on the same computer you play on, but it's not at all recommended, especially if you don't have it on an SSD.