essentially, yes.
I set up a chroot running a debian based minimal distro with opensshd running inside on a custom port number, with unique 4096bit keys, and a post-it stuck on top for what root's password in the chroot is. Otherwise the router will still act like a router. I can configure it to automatically start a game host daemon from that chroot using a limited user account-- or any other linux network daemon you want, like a cups server, or whatever. The opensshd instance is to give you access to the chroot's administration shell. It will be console only, but if you are a linux junkie, you can do all kinds of stuff with that. I would need to set it up to configure the desired deamons and the like anyway, and pass on the functionality as a friendly service.
In the case of a router, since I would have to recompile from router source anyway to get the boot hook to stick, I would also give you a nice selection of loadable kernel modules built as well, and turn on anonymous paging (swapfile use). It makes compile time take forever, but lets you load some of the more exotic USB device drivers if you want. Normally not enabled in stock systems due to space constraints, but with a chroot, we have all the space on the usb stick stuck in it. Means you could attach a USB audio device and use it like an internet radio if you want--- or put a linux supported USB video adapter on, and (try) to drive a GUI, or native shell. Also lets you support more filesystem types than the default ones that get baked in, so if you want EXT4, or XFS, or even Reiser (for some reason), you can get them.
Just keep in mind that routers tend to have very little memory, and would be abusing the shit out of swap if you try to load them down hard. The CPUs in them tend to be weak kneed as well, so daemons with heavy requirements arent really well suited.
NAS boxes on the other hand, tend to have a much more useful complement of RAM and CPU, (512mb and 800mhz on the low end), and have a real spinny disk inside for swap. They can run more aggressive daemons.