Yeah, you definitely should run it on a separate machine. A home NAS itself probably shouldn’t be doing anything beyond serving files and basic maintenance. Using them for too much will reduce their ability to serve data fast enough. Just be sure the media server and NAS have appropriate network cards, preferably gigabit, though even 100Mbit probably is enough for most of your network isn’t already too busy, and ideally are connected to the same switch (again preferably gigabit) with good quality network cables.